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2008 Fiscal Year Final Research Report

Stochastic analysis in infinite dimensional spaces

Research Project

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Project/Area Number 17340036
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKyoto University

Principal Investigator

SHIGEKAWA Ichiro  Kyoto University, 大学院・理学研究科, 教授 (00127234)

Co-Investigator(Kenkyū-buntansha) KUMAGAI Takashi  京都大学, 大学院・理学研究科, 教授 (90234509)
Co-Investigator(Renkei-kenkyūsha) YOSHIDA Nobuo  京都大学, 大学院・理学研究科, 准教授 (40240303)
HINO Masanori  京都大学, 大学院・情報学研究科, 准教授 (40303888)
UEKI Naomasa  京都大学, 大学院・人間環境学研究科, 准教授 (80211069)
AIDA Shigeki  大阪大学, 大学院・基礎工学研究科, 教授 (90222455)
UEMURA Hideaki  愛知教育大学, 教育学部, 教授 (30203483)
TAKANOBU Satoshi  金沢大学, 理学部, 教授 (40197124)
Project Period (FY) 2005 – 2008
KeywordsWiener 空間 / Brown 運動 / 拡散過程 / 対数Sobolev 不等式 / スペクトルギャップ / 格子スピン系 / Hodge-Kodaira 作用素
Research Abstract

確率解析に関する研究を、主に関数解析的な手法で進めた。ここでは次のような結果を得た。(1)Hodge-Kodaira 作用素のmultiplier の L^p 有界性(2)Riemann 多様体上のSchrodinger 作用素に対する Littlewood-Paleyの不等式(3)作用素の交換関係と生成作用素(4)Wiener空間及び格子スピン系のSchrodinger作用素のスペクトルギャップの存在(5)1次元拡散過程の生き残り拡散過程の存在(6)非対称な半群に関する超縮小性のための条件と、リーマン多様体上の拡散過程への応用。

  • Research Products

    (31 results)

All 2008 2007 2006 2005

All Journal Article (19 results) (of which Peer Reviewed: 19 results) Presentation (12 results)

  • [Journal Article] Weighted Poincare inequality and heat kernel estimates for finite range jump processes2008

    • Author(s)
      Chen, Z-Q., Kim, P., Kumagai, T
    • Journal Title

      Math. Ann 342, no.4

      Pages: 833-883

    • Peer Reviewed
  • [Journal Article] Heat kernel estimates for jump processes of mixed types on metric measure spaces2008

    • Author(s)
      Chen, Z-Q. and Kumagai, T
    • Journal Title

      Probab. Theory Related Fields 140, no.1-2

      Pages: 277-317

    • Peer Reviewed
  • [Journal Article] Log-Sobolev inequalities with potential functions on pinned path groups2008

    • Author(s)
      Aida, S
    • Journal Title

      Commun. Stoch. Anal 2, no.1

      Pages: 33-51

    • Peer Reviewed
  • [Journal Article] Central limit theorem for branching random walks in random environment2008

    • Author(s)
      Yoshida, N
    • Journal Title

      Ann. Appl. Probab 18, no.4

      Pages: 1619-1635

    • Peer Reviewed
  • [Journal Article] Phase Transitions for the Growth Rate of Linear Stochastic Evolutions2008

    • Author(s)
      Yoshida, N
    • Journal Title

      J. Stat. Phys 133, No.6

      Pages: 1033-1058

    • Peer Reviewed
  • [Journal Article] Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures2008

    • Author(s)
      Uemura, H
    • Journal Title

      Stochastic Process. Appl 118, no.10

      Pages: 1870-1891

    • Peer Reviewed
  • [Journal Article] Wegner estimate and localization for random magnetic fields2008

    • Author(s)
      Ueki, N
    • Journal Title

      Osaka J. Math 45, no.3

      Pages: 565-608

    • Peer Reviewed
  • [Journal Article] Schrodinger operators on the Wiener space2007

    • Author(s)
      Shigekawa, I
    • Journal Title

      Commun. Stoch. Anal 1, no.1

      Pages: 1-17

    • Peer Reviewed
  • [Journal Article] Semi-classical limit of the bottom of spectrum of a Schrodinger operator on a path space over a compact Riemannian manifold2007

    • Author(s)
      Aida, S
    • Journal Title

      J. Funct. Anal 251, no.1

      Pages: 59-121

    • Peer Reviewed
  • [Journal Article] Positive continuous additive functionals of multidimensional Brownian motion and the Brownian local time2007

    • Author(s)
      Uemura, H
    • Journal Title

      J. Math. Kyoto Univ 47, no.2

      Pages: 371-390

    • Peer Reviewed
  • [Journal Article] The probability of two F_ q-polynomials to be coprime2007

    • Author(s)
      Sugita, H., Takanobu, S
    • Journal Title

      Probability and number theory Kanazawa 2005 49

      Pages: 455-478

    • Peer Reviewed
  • [Journal Article] Defective intertwining property and generator domain2006

    • Author(s)
      Shigekawa, I
    • Journal Title

      J. Funct. Anal 239, no.2

      Pages: 257-274

    • Peer Reviewed
  • [Journal Article] On equivalence of L^p-norms related to Schrodinger type operators on Riemannian manifolds2006

    • Author(s)
      Miyokawa, T, Shigekawa, I
    • Journal Title

      Probab. Theory Related Fields 135, no.4

      Pages: 487-519

    • Peer Reviewed
  • [Journal Article] A trace theorem for Dirichlet forms on fractals2006

    • Author(s)
      Hino, M., Kumagai, T
    • Journal Title

      J. Funct. Anal 238, no.2

      Pages: 578-611

    • Peer Reviewed
  • [Journal Article] L^p multiplier theorem for the Hodge-Kodaira operator2005

    • Author(s)
      Shigekawa, I
    • Journal Title

      Seminaire de Probabilites XXXVIII 1857

      Pages: 226-246

    • Peer Reviewed
  • [Journal Article] Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs2005

    • Author(s)
      Barlow, M. T., Coulhon, T., Kumagai, T
    • Journal Title

      Comm. Pure Appl. Math 58, no.12

      Pages: 1642-1677

    • Peer Reviewed
  • [Journal Article] Construction of diffusion processes on fractals, dsets, and general metric measure spaces2005

    • Author(s)
      Kumagai, T., Sturm, K-T
    • Journal Title

      J. Math. Kyoto Univ 45, no.2

      Pages: 307-327

    • Peer Reviewed
  • [Journal Article] On singularity of energy measures on self-similar sets2005

    • Author(s)
      Hino, M
    • Journal Title

      Probab. Theory Related Fields 132, no.2

      Pages: 265-290

    • Peer Reviewed
  • [Journal Article] Small-time asymptotic estimates in local Dirichlet spaces2005

    • Author(s)
      Ariyoshi, T., Hino, M
    • Journal Title

      Electron. J. Probab 10, no.37

      Pages: 1236-1259

    • Peer Reviewed
  • [Presentation] Heat kernel estimates for recurrent random walk on random media2008

    • Author(s)
      Kumagai, T
    • Organizer
      Random systems from physics to biology
    • Place of Presentation
      Technical University of Berlin
    • Year and Date
      20080300
  • [Presentation] Non-symmetric diffusions on Riemannian manifolds and the ultracontractivity2008

    • Author(s)
      重川一郎
    • Organizer
      科研費シンポジウム「確率解析とその周辺」
    • Place of Presentation
      名古屋大学ベンチャー, ビジネス, ラボラトリー, ベンチャーホール
    • Year and Date
      2008-11-20
  • [Presentation] Ultracontractivity for nonsymmetric Markovian semigroup2008

    • Author(s)
      Shigekawa, I
    • Organizer
      German-Japanese Symposium on Stochastic Analysis and Applications 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-12
  • [Presentation] Uniqueness of Brownian motion on Sierpinski carpets2008

    • Author(s)
      Kumagai, T
    • Organizer
      Stochastic Analysis and Applications 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-11
  • [Presentation] Semi-classical limit of P(φ)_2 Hamiltonians2008

    • Author(s)
      Aida, S
    • Organizer
      German-Japanese Symposium on Stochastic Analysis and Applications 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-10
  • [Presentation] Energy measures and derivatives on some fractals2008

    • Author(s)
      Hino, M
    • Organizer
      German-Japanese Symposium on Stochastic Analysis and Applications 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-09
  • [Presentation] Non symmetric diffusions on a Riemannian manifold2008

    • Author(s)
      Shigekawa, I.
    • Organizer
      The 1st MSJ-SI, Probabilistic Approach to Geometry
    • Place of Presentation
      京都大学時計台百周年記念ホール
    • Year and Date
      2008-08-08
  • [Presentation] Semigoups that preserve a convex set in a Banach space2008

    • Author(s)
      Shigekawa, I
    • Organizer
      The 6th Workshop on Markov processes and related topics
    • Place of Presentation
      Anhui Normal University, Wuhu, CHINA
    • Year and Date
      2008-07-21
  • [Presentation] The dual ultracontractivity and its applications, Dirichlet Forms2007

    • Author(s)
      Shigekawa, I
    • Organizer
      Stochastic Analysis and Interacting Systems
    • Place of Presentation
      Technical University of Berlin, Berlin, GERMANY
    • Year and Date
      2007-09-21
  • [Presentation] Heat kernel estimates and Harnack inequalities for jump processes2006

    • Author(s)
      熊谷隆
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      20061200
  • [Presentation] Random walk on the incipient infinite cluster for oriented percolation in high dimensions2006

    • Author(s)
      Kumagai, T
    • Organizer
      AMS Sectional Meeting
    • Place of Presentation
      Connecticut 大学, 米国
    • Year and Date
      2006-10-28
  • [Presentation] One dimensional diffusions conditioned to be non-explosive2006

    • Author(s)
      Shigekawa, I
    • Organizer
      Mini Symposium 24 "Probability and Geometry," Jahrestagung der Deutsche Mathematiker-Verinigung
    • Place of Presentation
      University of Bonn, Bonn, GERMANY
    • Year and Date
      2006-09-22

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Published: 2010-06-10   Modified: 2016-04-21  

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