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New development of infinite dimensional stochastic analysis and its applications

Research Project

Project/Area Number 21244009
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTohoku University (2010-2011)
Osaka University (2009)

Principal Investigator

AIDA Shigeki  東北大学, 大学院・理学研究科, 教授 (90222455)

Co-Investigator(Kenkyū-buntansha) SHIGEKAWA Ichiro  京都大学, 大学院理学研究科, 教授 (00127234)
MATSUMOTO Hiroyuki  青山学院大学, 理工学部, 教授
HANDA Kenji  佐賀大学, 大学院工学研究科, 准教授 (10238214)
KAWABI Hiroshi  岡山大学, 自然科学研究科, 准教授 (80432904)
INAHAMA Yuzuru  名古屋大学, 大学院多元数理科学研究科, 准教授 (80431998)
NAGAHATA Yukio  新潟大学, 自然科学系, 准教授 (50397725)
YANO Kouji  京都大学, 大学院理学研究科, 准教授 (80467646)
Co-Investigator(Renkei-kenkyūsha) HINO Masanori  大阪大学, 大学院基礎工学研究科, 教授 (40303888)
KOHATSU-HIGA Arturo  立命館大学, 理工学部, 教授 (80420412)
HIROSHIMA Fumio  九州大学, 大学院数理学研究院, 教授 (00330358)
TANIGUCHI Setsuo  九州大学, 大学院数理学研究院, 教授 (70155208)
HARIYA Yuu  東北大学, 大学院理学研究科, 准教授 (20404030)
NINOMIYA Shoiti  東京工業大学, 大学院イノベーションマネジメント研究科, 教授 (70313377)
TAKANOBU Satoshi  金沢大学, 理工研究域数物科学系, 教授 (40197124)
OHTA Shin-ichi  京都大学, 大学院理学研究科, 准教授 (00372558)
MIKAMI Toshio  広島大学, 大学院工学研究科, 教授 (70229657)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥19,760,000 (Direct Cost: ¥15,200,000、Indirect Cost: ¥4,560,000)
Fiscal Year 2011: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2010: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2009: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Keywords確率解析 / 場の量子論 / ラフパス解析 / ループ空間 / 準古典極限 / 最適輸送写像 / 確率測度の幾何学 / 処罰問題 / ループ群 / 確率微分方程式 / アレクサンドロ / 超縮小性 / アレクサンドロフ空間 / 新古典不等式
Research Abstract

The study subjects and results are as follows: (1) Laplace approximation and the vanishing of L^2-cohomologies of loop groups from the view point of rough path analysis, (2) Studies on semi-classical properties of Hamiltonian in quantum field theory, Studies from the view point of functional integration, (3)Basic results on the geometry of the space of probability measures (4)Basic study on Sobolev spaces on H-convex set in Wiener spaces and penalization problem and basic results for probability theory

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (130 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (74 results) (of which Peer Reviewed: 74 results) Presentation (52 results) (of which Invited: 11 results) Book (3 results) Remarks (1 results)

  • [Journal Article] Laplace approximation for rough differential equation driven by fractional Brownian motion2013

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Ann. Probab

      Volume: 41 Issue: 1 Pages: 170-205

    • DOI

      10.1214/11-aop733

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A moment estimate for the derivative process in rough path theory2012

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Proc. Amer.Math.Soc

      Volume: 140 Issue: 6 Pages: 2183-2191

    • DOI

      10.1090/s0002-9939-2011-11051-7

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The sector constants of continuous state branching processes with immigration2012

    • Author(s)
      Kenji Handa
    • Journal Title

      J.Funct.Anal

      Volume: 262 Issue: 10 Pages: 4488-4524

    • DOI

      10.1016/j.jfa.2012.02.026

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions2012

    • Author(s)
      Sergio Albeverio, Hiroshi Kawabi and Michael Roeckner
    • Journal Title

      J.Funct.Anal

      Volume: 262 Issue: 2 Pages: 602-638

    • DOI

      10.1016/j.jfa.2011.09.023

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Absence of ground state of the Nelson model with variable coefficients2012

    • Author(s)
      C.Gerard, F.Hiroshima, A.Pannati and A.Suzuki
    • Journal Title

      J.Funct.Anal

      Volume: 262 Issue: 1 Pages: 273-299

    • DOI

      10.1016/j.jfa.2011.09.010

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts, Ann. Inst2012

    • Author(s)
      Arturo Kohatsu-Higa
    • Journal Title

      Henri Poincare Probab. Stat

      Volume: 48 Issue: 3 Pages: 871-883

    • DOI

      10.1214/11-aihp418

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maxima and minima of overall survival functions with fixed marginal distributions and transmission of technology2012

    • Author(s)
      Isao Higuchi and Toshio Mikami
    • Journal Title

      Communications in Statistics-Theory and Methods

      Volume: 41 Issue: 1 Pages: 46-61

    • DOI

      10.1080/03610926.2010.513788

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] COH-formula and Dirichlet Laplacians on small domains of pinned path spaces2011

    • Author(s)
      Shigeki Aida
    • Journal Title

      Contemporary Mathematics

      Volume: 545 Pages: 1-12

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Vanishing of one-dimensional L^2 cohomologies of loop groups2011

    • Author(s)
      Shigeki Aida
    • Journal Title

      J.Funct.Anal

      Volume: 261 Issue: 8 Pages: 2164-2213

    • DOI

      10.1016/j.jfa.2011.06.003

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infrared problem for the Nelson model on static space-time, Comm2011

    • Author(s)
      C.Gerard, F.Hiroshima, A.Pannati and A.Suzuki
    • Journal Title

      Math. Physics

      Volume: 308 Issue: 2 Pages: 543-566

    • DOI

      10.1007/s00220-011-1289-7

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semigroups preserving a convex set in a Banach space2011

    • Author(s)
      Ichiro Shigekawa
    • Journal Title

      Kyoto J.Math

      Volume: 51 Issue: 3 Pages: 647-672

    • DOI

      10.1215/21562261-1299918

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dirichlet spaces on H-convex sets in Wiener space2011

    • Author(s)
      Masanori Hino
    • Journal Title

      Bull.Sci.Math

      Volume: 135 Issue: 6-7 Pages: 667-683

    • DOI

      10.1016/j.bulsci.2011.07.008

    • NAID

      120003437141

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bernoulli polynomials, and Levy's stochastic area formula, Bull2011

    • Author(s)
      N.Ikeda and Setsuo Taniguchi, Euler polynomials
    • Journal Title

      Sci. Math

      Volume: 135 Issue: 6-7 Pages: 684-694

    • DOI

      10.1016/j.bulsci.2011.07.009

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral gap for multi-species exclusion processes2011

    • Author(s)
      Yukio Nagahata and Makiko Sasada
    • Journal Title

      J. Stat. Physics

      Volume: 143 Pages: 381-398

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Displacement convexity of generalized relative entropies2011

    • Author(s)
      Shin-ichi Ohta and Asuka Takatsu
    • Journal Title

      Adv. Math

      Volume: 228 Issue: 3 Pages: 1742-1787

    • DOI

      10.1016/j.aim.2011.06.029

    • NAID

      120003405527

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wiener integral for the coordinate process under the sigma-finite measure unifying Brownian penalisations.2011

    • Author(s)
      Kouji Yano
    • Journal Title

      ESAIM Probab. Sta.

      Volume: 15 Pages: 69-84

    • DOI

      10.1051/ps/2010024

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a zero-one law for the norm process of transient random walk2011

    • Author(s)
      A. Matsumoto and K.Yano
    • Journal Title

      Seminaire de Probabilites

      Volume: XLIII Pages: 757-798

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral gap for multi-species exclusion processes2011

    • Author(s)
      Yukio Nagahata
    • Journal Title

      Journal of Statistical Physics

      Volume: 143 Issue: 2 Pages: 381-398

    • DOI

      10.1007/s10955-011-0176-0

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] COH formula and Dirichlet Laplacians on small domains of pinnedpath spaces2011

    • Author(s)
      Shigeki Aida
    • Journal Title

      Concentration, functional inequalities and isoperi metry (a volume in Contemporary mathematics)

      Volume: 545(In press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a zero-one law for the norm process of transient random walk2011

    • Author(s)
      A.Matsumoto, K.Yano
    • Journal Title

      Seminaire de Probabilites XLIII

      Volume: 2006 Pages: 757-798

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maxima and minima of overall survival functions with fixed marginal distributions and transmission of technology2011

    • Author(s)
      I.Higuchi, Toshio Mikami
    • Journal Title

      Communications in Statistics-Theory and Methods-

      Volume: (未定)(In press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rough path analysis: An introduction2010

    • Author(s)
      Shigeki Aida
    • Journal Title

      Adv.Stud.Pure Math

      Volume: 57 Pages: 1-28

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on rough differential equations with unbounded diffusion coefficients2010

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Adv.Stud.Pure Math

      Volume: 57 Pages: 155-170

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-symmetric diffusions on a Riemannian manifold2010

    • Author(s)
      Ichiro Shigekawa
    • Journal Title

      Adv.Stud.Pure Math

      Volume: 57 Pages: 437-461

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space2010

    • Author(s)
      Masanori Hino
    • Journal Title

      J.Funct.Anal

      Volume: 258 Issue: 5 Pages: 1656-1681

    • DOI

      10.1016/j.jfa.2009.06.033

    • NAID

      120001759396

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fractional order Taylor's series and the neo-classical inequality2010

    • Author(s)
      Keisuke Hara and Masanori Hino
    • Journal Title

      Bull.Lond.Math.Soc

      Volume: 42 Issue: 3 Pages: 467-477

    • DOI

      10.1112/blms/bdq013

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Ito-Nisio theorem, quadratic Wiener functionals and 1-solitons2010

    • Author(s)
      Nobuyuki Ikeda and Setsuo Taniguchi
    • Journal Title

      Stoch.Proc.Appl

      Volume: 120 Issue: 5 Pages: 605-621

    • DOI

      10.1016/j.spa.2010.01.009

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Penalisation of a stable Levy process involving its one-sided supremum2010

    • Author(s)
      Kouji Yano
    • Journal Title

      Ann. Inst. Henri Poincare Probab

      Volume: 46 Issue: 4 Pages: 1042-1054

    • DOI

      10.1214/09-aihp339

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Excursions away from a regular point for one dimensional symmetric Levy processes without Gaussian part2010

    • Author(s)
      Kouji Yano
    • Journal Title

      Potential anal

      Volume: 32 Issue: 4 Pages: 305-341

    • DOI

      10.1007/s11118-009-9152-6

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cameron-Martin formula for theσ-finite measure unifying Brownian penalisations2010

    • Author(s)
      Kouji Yano
    • Journal Title

      J. Funct. Anal.

      Volume: 258 Issue: 10 Pages: 3492-3516

    • DOI

      10.1016/j.jfa.2009.11.021

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal transport and Ricci curvature in Finsler geometry2010

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 57 Pages: 475-516

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limiting behaviors of the Brownian motions on hyperbolic spaces Colloquim Mathematicum2010

    • Author(s)
      Hiroyuki Matsumoto
    • Volume
      119
    • Pages
      475-516
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A stochastic Taylor-like expansion in the rough path theory2010

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      J. Theoret. Probab

      Volume: 23 Issue: 3 Pages: 671-714

    • DOI

      10.1007/s10959-010-0287-6

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lower bounds for densities of Asian type stochastic differential equations2010

    • Author(s)
      Vlad Bally and Arturo Kohatsu-Higa
    • Journal Title

      J. Funct. Anal

      Volume: 258 Issue: 9 Pages: 3134-3164

    • DOI

      10.1016/j.jfa.2009.10.027

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Localization for a class of linear systems2010

    • Author(s)
      Yukio Nagahata and Nobuo Yoshida
    • Journal Title

      Electron.J.Probab

      Volume: 15 Issue: none Pages: 636-653

    • DOI

      10.1214/ejp.v15-757

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral gap for zero-range processes with jump rate g(x)=x^γ2010

    • Author(s)
      Yukio Nagahata
    • Journal Title

      Stochastic Process. Appl

      Volume: 120 Issue: 6 Pages: 949-958

    • DOI

      10.1016/j.spa.2010.01.019

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rough path analysis, An introduction2010

    • Author(s)
      Shigeki Aida
    • Journal Title

      Advanced studies in pure mathematics

      Volume: 57 Pages: 1-28

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-symmetric diffusions on a Riemannian manifold2010

    • Author(s)
      Ichiro Shigekawa
    • Journal Title

      Advanced studies in pure mathematics

      Volume: 57 Pages: 437-461

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sets of finite perimeter and the Hausdorff--Gauss measure on the Wiener space2010

    • Author(s)
      Masanori Hino
    • Journal Title

      Journal of Functional Analysis

      Volume: 258 Pages: 1656-1681

    • NAID

      120001759396

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fractional order Taylor's series and the neo-classical inequality2010

    • Author(s)
      Keisuke Hara, Masanori Hino
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 42 Pages: 467-477

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Ito-Nisio theorem, quadratic Wiener functionals, and 1-solitons2010

    • Author(s)
      Nobuyuki Ikeda, Setsuo Taniguchi
    • Journal Title

      Stoch.Proc.Appl.

      Volume: 120 Pages: 605-621

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Penalisation of a stable Levy process involving its one-sided supremum2010

    • Author(s)
      K.Yano, Y.Yano, M.Yor
    • Journal Title

      Ann.Inst.Henri Poincare Probab.Stat.

      Volume: 46 Pages: 1042-1054

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal transport and Ricci curvature, in Finsler geometry2010

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Advanced studies in pure mathematics

      Volume: 57 Pages: 475-516

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limiting behaviors of the Brownian motions on hyperbolic spaces2010

    • Author(s)
      Hiroyuki Matsumoto
    • Journal Title

      Colloquim Mathematicum

      Volume: 119 Pages: 193-215

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A stochastic Taylor-like expansion in the rough path theory2010

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      J.Theoret.Probab.

      Volume: 23 Pages: 671-714

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lower bounds for densities of Asian type stochastic differential equations2010

    • Author(s)
      V.Bally, A.Kohatsu-Higa
    • Journal Title

      Journal of Functional Analysis

      Volume: 258 Pages: 3134-3164

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Localization for a class of linear systems2010

    • Author(s)
      Yukio Nagahata, Nobuo Yoshida
    • Journal Title

      Electronic Journal of Probability

      Volume: 15 Pages: 636-653

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral gap for zero-range processes with jump rate $g(x)=x^{\gamma}$2010

    • Author(s)
      Yukio Nagahata
    • Journal Title

      Stochastic Processes and their Application

      Volume: 120 Pages: 949-958

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-classical limit of the lowest eigenvalue of a Schrodinger operator on a Wiener space : I. Unbounded one particle Hamiltonians2010

    • Author(s)
      Shigeki Aida
    • Journal Title

      Asterisque (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rough path analysis, An introduction2010

    • Author(s)
      Shigeki Aida
    • Journal Title

      Advanced studies in pure mathematics (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener space2010

    • Author(s)
      Masanori Hino
    • Journal Title

      Journal of Functional Analysis 258

      Pages: 1656-1681

    • NAID

      120001759396

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fractional order Taylor's series and the neo-classical inequality2010

    • Author(s)
      Keisuke Hara, Masanori Hino
    • Journal Title

      Bulletin of the London Mathematical Society (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-symmetric diffusions on a Riemannian manifold2010

    • Author(s)
      I.Shigekawa
    • Journal Title

      Advanced Studies in Pure Mathematics (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on rough differential equation with unbounded coefficients2010

    • Author(s)
      Y.Inahama
    • Journal Title

      Advanced Studies in Pure Mathematics (In press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-classical limit of the lowest eigenvalue of a Schrodinger operator on a Wiener space: II.P(φ)_2 -model on a finite volume2009

    • Author(s)
      Shigeki Aida
    • Journal Title

      J.Funct.Anal

      Volume: 256 Issue: 10 Pages: 3342-3367

    • DOI

      10.1016/j.jfa.2008.10.001

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A WIENER INTEGRAL APPROACH TO NON-COMMUTATIVE HARMONIC OSCILLATORS2009

    • Author(s)
      Setsuo Taniguchi
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 63 Issue: 2 Pages: 347-352

    • DOI

      10.2206/kyushujm.63.347

    • NAID

      130000135289

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the laws of first hitting times of points for one-dimensional symmetric stable Levy processes2009

    • Author(s)
      Kouji Yano, Y.Yano and M.Yor
    • Journal Title

      Seminaire de Probabilites

      Volume: 42 Pages: 187-227

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Penalising symmetric stable Lévy paths2009

    • Author(s)
      Kouji Yano
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 61 Issue: 3 Pages: 757-798

    • DOI

      10.2969/jmsj/06130757

    • NAID

      10026998447

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gradient flows on Wasserstein spaces over compact Alexandrov spaces, Amer2009

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      J.Math

      Volume: 131 Issue: 2 Pages: 475-516

    • DOI

      10.1353/ajm.0.0048

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniform convexity and smoothness, and their applications in Finsler geometry2009

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Math.Ann

      Volume: 343 Issue: 3 Pages: 669-699

    • DOI

      10.1007/s00208-008-0286-4

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tree structured independence for exponential Brownian functionals, Stochastic Process2009

    • Author(s)
      Hiroyuki Matsumoto, J.Weso.owski and P.Witkowski
    • Journal Title

      Appl

      Volume: 119 Issue: 10 Pages: 3793-3815

    • DOI

      10.1016/j.spa.2009.07.008

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The two-parameter Poisson-Dirichlet point process2009

    • Author(s)
      Kenji Handa
    • Journal Title

      Bernoulli

      Volume: 15 Pages: 1082-1116

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semi-classical limit of the lowest eigenvalue of a Schrodinger operator on a Wiener space : II. P(φ)_2-model on a finite volume2009

    • Author(s)
      Shigeki Aida
    • Journal Title

      Journal of Functional Analysis 256

      Pages: 3342-3367

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Wiener integral approach to non-commutative harmonic oscillators2009

    • Author(s)
      Setsuo Taniguchi
    • Journal Title

      Kyushu Jour.Math. 63-2

      Pages: 347-352

    • NAID

      130000135289

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the laws of first hitting times of points for one-dimensional symmetric stable L\'evy processes2009

    • Author(s)
      K.Yano, Y.Yano, M.Yor
    • Journal Title

      S\' eminaire de Probabilit\'es 42

      Pages: 187-227

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Penalising symmetric stable L\'evy paths2009

    • Author(s)
      K.Yano, Y.Yano, M.Yor
    • Journal Title

      J.Math.Soc.Japan 61

      Pages: 757-798

    • NAID

      10026998447

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gradient flows on Wasserstein spaces over compact Alexandrov spaces2009

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Amer.J.Math. 131

      Pages: 475-516

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniform convexity and smoothness, and their applications in Finsler geometry2009

    • Author(s)
      Shin-ichi Ohta
    • Journal Title

      Math.Ann. 343

      Pages: 669-699

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tree structured independence for exponential Brownian functionals2009

    • Author(s)
      Hiroyuki Matsumoto, J.Weso\lowski, P.Witkowski
    • Journal Title

      Stoch.Proc.Appl. 119

      Pages: 3798-3815

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The two-parameter Poisson-Dirichlet point process2009

    • Author(s)
      Kenji Handa
    • Journal Title

      Bernoulli 15

      Pages: 1082-1116

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimating Multidimensional Density Functions using the Malliavin-Thalmaier Formula2009

    • Author(s)
      A.Kohatsu-Higa, K.Yasuda
    • Journal Title

      SIAM Journal on Numerical Analysis 47

      Pages: 1546-1575

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Central limit theorem for a class of linear systems2009

    • Author(s)
      Y.Nagahata, N.Yoshida
    • Journal Title

      Electronic Journal of Probability 14

      Pages: 960-977

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A moment estimate for the derivative process in rough path theory

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: (未定)(In press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Infrared problem for the Nelson model with variable coefficients

    • Author(s)
      C.Gerard, F.Hiroshima, A.Pnati, A.Suzuki
    • Journal Title

      Communucations in Mathematical Physics

      Volume: (未定)(In press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Poincare's lemma on domains defined by Brownian rough path2012

    • Author(s)
      Shigeki Aida
    • Organizer
      Rough path analysis and related topics
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Tunneling for spatially cut-off P(φ)_2-Hamiltonians2012

    • Author(s)
      Shigeki Aida
    • Organizer
      Stochastic Analysis and Stochastic PDEs
    • Place of Presentation
      イギリス・ウォーリック大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] An estimate of spectral gap for simple exclusion process with degenerate rates2012

    • Author(s)
      Yukio Nagahata
    • Organizer
      数理物理と確率解析
    • Place of Presentation
      湘南国際村センター
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Wright-Fisher拡散モデルのジャンプ過程版について2012

    • Author(s)
      Kenji Handa
    • Organizer
      数理物理と確率解析
    • Place of Presentation
      湘南国際村センター
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Tunneling for spatially cut-off P(φ)_2-Hamiltonian2011

    • Author(s)
      Shigeki Aida
    • Organizer
      Stochastic analysis and its application
    • Place of Presentation
      Bonn, GERMANY
    • Year and Date
      2011-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Dirichlet spaces on H-convex sets in the Wiener space2011

    • Author(s)
      Masanori Hino
    • Organizer
      マルコフ過程と関連する話題
    • Place of Presentation
      関西大学
    • Year and Date
      2011-01-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] Semi-classical limit of the generalized second lowest eigenvalue of Dirichlet Laplacians on small domains in path spaces2011

    • Author(s)
      Shigeki Aida
    • Organizer
      伊都確率論シンポジウム
    • Place of Presentation
      九州大学
    • Year and Date
      2011-01-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Tunneling for spatially cut-off P(φ)_2-Hamiltonians2011

    • Author(s)
      Shigeki Aida
    • Organizer
      Stochastic analysis and its applications
    • Place of Presentation
      ドイツ・ボン大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Tunneling for spatially cut-off P(φ)_2-Hamiltonians2011

    • Author(s)
      Shigeki Aida
    • Organizer
      変分問題の展開-確率論と交錯する変分問題ー
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Stochastic Partial Differential Equations and Related Topics
    • Place of Presentation
      陳省身数学研究所, 南開大学 (中国)
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Precise asymptotics of functional integrals for infinite dimensional Ito-Lyons map of Brownian rough paths2011

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      The 35th Conference on Stochastic Processes and their Applications
    • Place of Presentation
      メキシコ Oaxaca
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] 半群のマルコフ性とその周辺2011

    • Author(s)
      Ichiro Shigekawa
    • Organizer
      仙台シンポジウム
    • Place of Presentation
      東北大学大学院情報科学研究科
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] The spectrum of non-symmetric operators and Markov processes2011

    • Author(s)
      Ichiro Shigekawa
    • Organizer
      5th International Conference on Stochastic Analysis and Its Applications
    • Place of Presentation
      ドイツ・ボン大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Dirichlet過程とPoisson-Dirichlet分布について2011

    • Author(s)
      Kenji Handa
    • Organizer
      官庁統計データの公開における諸問題の研究と他分野への応用
    • Place of Presentation
      統計数理研究所
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Short time kernel asymptotics for Young SDE driven by fractional Brownian motion by means of Watanabe distribution theory2011

    • Author(s)
      Yuzuru Inahama
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      佐賀大学
    • Related Report
      2011 Annual Research Report
  • [Presentation] Strong uniqueness of diffusions to Gibbs measures on a path space with exponential interactions2010

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      岡山大学理学部
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Non-contraction of heat flow on Minkowski spaces2010

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      ERC Workshop on Optimal Transportation and Applications
    • Place of Presentation
      Centro De Giorgi, Pisa, ITALY
    • Year and Date
      2010-10-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] Martingale dimensions and derivatives for some fractals2010

    • Author(s)
      Masanori Hino
    • Organizer
      Conference in Memory of Paul Malliavin
    • Place of Presentation
      Universite de Bourgogne, FRANCE
    • Year and Date
      2010-10-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Martingale dimensions for self-similar fractals2010

    • Author(s)
      Masanori, Hino
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      大阪
    • Year and Date
      2010-09-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Displacement convexity of generalized relative entropies2010

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      千里ライフサイエンスセンタービル
    • Year and Date
      2010-09-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Spectral analysis of OFT by functional integration with jump processes2010

    • Author(s)
      Fumio Hiroshima
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      千里ライフサイエンスセンタービル
    • Year and Date
      2010-09-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Martingale dimensions for self-similar fractals2010

    • Author(s)
      Masanori Hino
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      千里ライフサイエンスセンタービル
    • Year and Date
      2010-09-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Laplace-type asymptotics for rough differential equation driven by fractional Brownian motion2010

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The 34th conference on stochastic processes and their applications
    • Place of Presentation
      千里ライフサイエンスセンタービル
    • Year and Date
      2010-09-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] COH formula and Dirichlet Laplacians on small domains of pinned path spaces2010

    • Author(s)
      Shigeki Aida
    • Organizer
      34^<th> conference of SPA
    • Place of Presentation
      大阪
    • Year and Date
      2010-09-07
    • Related Report
      2011 Final Research Report
  • [Presentation] COH formula and Dirichlet Laplacians on small domains of pinned path spaces2010

    • Author(s)
      Shigeki Aida
    • Organizer
      34th Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      千里ライフサイエンスセンタービル
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Vanishing of one dimensional L^2-cohomologies of loop groups2010

    • Author(s)
      Shigeki Aida
    • Organizer
      4-th international conference on Stochastic Analysis and its Applications
    • Place of Presentation
      関西大学
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report
  • [Presentation] Vanishing of one dimensional L^2-cohomologies of loop groups2010

    • Author(s)
      Shigeki Aida
    • Organizer
      確率論と幾何学
    • Place of Presentation
      東北大学
    • Year and Date
      2010-08-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Laplace-type asymptotics for rough differential equation driven by fractional Brownian motion2010

    • Author(s)
      Yuzuru Inahama
    • Organizer
      ICM satellite conference on probability and stochastic processes
    • Place of Presentation
      Indian Institute of Statistics, INDIA
    • Year and Date
      2010-08-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] A Malliavin calculus method to study SDE's with irregular drifts2010

    • Author(s)
      A.Kohatsu-Higa
    • Organizer
      ICM Satellite Conference on Probability and Stochastic Processes
    • Place of Presentation
      Indian Statistical Institute, INDIA
    • Year and Date
      2010-08-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Ricci curvature and optimal transport2010

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      Oberseminar Differentialgeometrie
    • Place of Presentation
      Munster, GERMANY
    • Year and Date
      2010-07-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Precise asymptotics for infinite dimensional Ito-Lyons maps of Brownian rough paths2010

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      Rough Paths, SPDEs and Related Topics
    • Place of Presentation
      University of Cambridge, UK
    • Year and Date
      2010-04-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] On Dirichlet operators of exp(φ)_1-quantum fields in infinite volume2010

    • Author(s)
      Hiroshi Kawabi
    • Organizer
      First CIRM-HCM Joint Meeting : Stochastic Analysis, SPDEs, Particle Systems, Optimal Transport
    • Place of Presentation
      Levico Terme(イタリア)
    • Year and Date
      2010-01-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Vanishing of one dimensional L^2-cohomologies of loop groups2009

    • Author(s)
      Shigeki Aida
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-12-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Semi-classical limit of the lowest eigenvalue of P(φ)_2 Hamiltonian on a finite interval2009

    • Author(s)
      Shigeki Aida
    • Organizer
      数学的場の量子論とくりこみ理論
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2009-11-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Vanishing of one dimensional L^2-cohomologies of loop groups2009

    • Author(s)
      Shigeki Aida
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-06
    • Related Report
      2009 Annual Research Report
  • [Presentation] A rough path as a simple object and the problems, I and II2009

    • Author(s)
      Keisuke Hara
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] Log-Sobolev inequalities and semi-classical limit of P(φ)_2-Hamiltonians2009

    • Author(s)
      Shigeki Aida
    • Organizer
      国際研究集会Concentration, functional inequalities And isoperimetry
    • Place of Presentation
      Florida, USA
    • Year and Date
      2009-10-31
    • Related Report
      2011 Final Research Report
  • [Presentation] Log-Sobolev inequalities and semi-classical limit of P(φ)_2-Hamiltonians2009

    • Author(s)
      Shigeki Aida
    • Organizer
      International workshop on : "Concentration, functional inequalities and isoperimtry"
    • Place of Presentation
      Florida Atlantic University, Boca Raton, Florida (USA)
    • Year and Date
      2009-10-31
    • Related Report
      2009 Annual Research Report
  • [Presentation] プラウン処罸を統一するシグマ有限測度について2009

    • Author(s)
      矢野孝次
    • Organizer
      マルコフ過程と確率解析
    • Place of Presentation
      岡山大学
    • Year and Date
      2009-10-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] 新古典不等式について2009

    • Author(s)
      Masanori Hino
    • Organizer
      マルコフ過程と確率解析
    • Place of Presentation
      岡山大学
    • Year and Date
      2009-10-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] Spectral gap for multi-species exclusion processes2009

    • Author(s)
      Yukio Nagahata
    • Organizer
      VIIIth workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      東京大学
    • Year and Date
      2009-10-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Non-symmetric Diffusion on a Riemannian manifold2009

    • Author(s)
      Ichiro Shigekawa
    • Organizer
      33rd Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      Berlin, GERMANY.
    • Year and Date
      2009-07-31
    • Related Report
      2011 Final Research Report
  • [Presentation] Non-symmetric Diffusion on a Riemannian manifold2009

    • Author(s)
      Ichiro Shigekawa
    • Organizer
      33rd Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      TU Berlin, Berlin (GERMANY)
    • Year and Date
      2009-07-31
    • Related Report
      2009 Annual Research Report
  • [Presentation] Vanishing of one dimensional L^2 cohomologies of loop groups2009

    • Author(s)
      Shigeki Aida
    • Organizer
      33rd conference of SPA
    • Place of Presentation
      Berlin, GERMANY
    • Year and Date
      2009-07-30
    • Related Report
      2011 Final Research Report
  • [Presentation] Vanishing of one dimensional L^2-cohomologies of loop groups2009

    • Author(s)
      Shigeki Aida
    • Organizer
      33rd Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      ベルリン工科大(ドイツ)
    • Year and Date
      2009-07-30
    • Related Report
      2009 Annual Research Report
  • [Presentation] 移入を伴う分枝過程の定常分布について2009

    • Author(s)
      Kenji Handa
    • Organizer
      確率解析の理論と応用-さよなら箱崎
    • Place of Presentation
      九州大学
    • Year and Date
      2009-07-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Rough path analysis for an infinite dimensional diffusion2009

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The first Institute of Mathematical Statistics, Asia-Pacific Rim Meeting
    • Place of Presentation
      Seoul University, SOUTH KOREA
    • Year and Date
      2009-06-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Rough path analysis for an infinite dimensional diffusion2009

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The first IMS-APRM (Institute of Mathematical Statistics, Asia-Pacific Rim Meeting)
    • Place of Presentation
      Seoul University(韓国)
    • Year and Date
      2009-06-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Semi-classical limit of P(φ)_2-Hamiltonian2009

    • Author(s)
      Shigeki Aida
    • Organizer
      保存則と幾何学的偏微分方程式とその応用
    • Place of Presentation
      京大会館
    • Year and Date
      2009-06-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Approximations for SDE's drieven by Levy processes2009

    • Author(s)
      A.Kohatsu-Higa
    • Organizer
      Third Conference on Numerical Methods in Finance
    • Place of Presentation
      ENPC, Paris (France)
    • Year and Date
      2009-04-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Ricci curvature, entropy and optimal transport2009

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      Optimal Transportation: Theory and Applications
    • Place of Presentation
      Universite Joseph Fourier, Grenoble, FRANCE
    • Related Report
      2011 Final Research Report
  • [Presentation] Ricci curvature, entropy and optimal transport2009

    • Author(s)
      Shin-ichi Ohta
    • Organizer
      Optimal Transportation : Theory and Applications
    • Place of Presentation
      Universite Joseph Fourier, Grenoble (France)
    • Related Report
      2009 Annual Research Report
  • [Book] Feynman-Kac-Type Theorems and Gibbs measures on Path space. With applications to rigorous quantum field theory2011

    • Author(s)
      J.L.rinczi, Fumio Hiroshima, V.Betz
    • Publisher
      Walter de Gruyter Inc
    • Related Report
      2011 Final Research Report
  • [Book] Feynman-Kac-Type Theorems and Gibbs Measures on Path Space. With Applications into Rigorous Quantum Field Theory2011

    • Author(s)
      J.Lorinczi, F.Hiroshima, V.Betz (共同執筆)
    • Total Pages
      506
    • Publisher
      Walter de Gruyter
    • Related Report
      2011 Annual Research Report
  • [Book] 日本の現代数学2009

    • Author(s)
      会田茂樹
    • Publisher
      数学書房
    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.math.tohoku.ac.jp/~aida/index-j.html

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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