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Study of rough path theory

Research Project

Project/Area Number 22740061
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

INAHAMA Yuzuru  名古屋大学, 多元数理科学研究科, 准教授 (80431998)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsラフパス理論 / 確率微分方程式 / マリアヴァン解析 / 大偏差原理 / 漸近展開 / ラフパス / フラクショナル・ブラウン運動 / ラプラス近似 / フラクショナルブラウン運動
Research Abstract

I have studied rough path theory for these four years. This theory is a "de-randomization" of Ito's theory of stochastic differential equation and looks like real analysis, rather than probability theory. I studied probabilistic aspects of this rapidly growing research area, in particular, asymptotic theorems
such as large deviation principle and Laplace-type asymptotic expansions.
Using Malliavin calculus as a tool, I write a few papers on this topic.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (35 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (22 results) (of which Invited: 3 results) Remarks (2 results)

  • [Journal Article] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2014

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Transaction of American Mathematical Society

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Laplace approximation for rough differential equation driven by fractional Brownian motion2013

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Ann. Probab

      Volume: 41, No.1 Pages: 170-205

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [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
      2013 Annual Research Report 2012 Annual 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 Pages: 2183-2191

    • Related Report
      2013 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
    • Peer Reviewed
  • [Journal Article] Laplace approximation for rough differential equation driven by fractional Brownian motion2012

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Ann.Probab.

      Volume: (In press)

    • Related Report
      2011 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, Issue 3 Pages: 671-714

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on rough differential equations with unbounded coefficients, Probabilistic approach to geometry2010

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 57 Pages: 155-170

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A stochastic Taylor-like expansion in rough path theory2010

    • Author(s)
      Inahama, Y.
    • Journal Title

      J.Theoret.Probab.

      Volume: 23 Pages: 671-714

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes

    • Author(s)
      Yuzuru Inahama
    • Journal Title

      Trans. Amer. Math. Soc

      Volume: (To appear) Pages: 35-35

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A moment estimate for the derivative process in rough path theory

    • Author(s)
      Inahama, Y.
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: (未定)(印刷中)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2014

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Rough Paths : Theory and Applications. Institute for Pure and Applied Mathematics
    • Place of Presentation
      UCLA, Los Angeles, USA
    • Year and Date
      2014-01-30
    • Related Report
      2013 Final Research Report
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2014

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Rough Paths: Theory and Applications.
    • Place of Presentation
      IPAM, University of California (LA)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2013

    • Author(s)
      Yuzuru Inahama
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Year and Date
      2013-12-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2013

    • Author(s)
      Yuzuru Inahama
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      京都大学
    • Year and Date
      2013-09-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] ラフパス理論--反復積分の(確率)解析学--2013

    • Author(s)
      Yuzuru Inahama
    • Organizer
      日本数学会年会企画講演
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2013

    • Author(s)
      Yuzuru Inahama
    • Organizer
      新潟確率論ワークショップ
    • Place of Presentation
      新潟大学
    • Year and Date
      2013-01-26
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Large deviation principle for certain spatially lifted Gaussian rough path2013

    • Author(s)
      Yuzuru Inahama
    • Organizer
      マルコフ過程と確率解析
    • Place of Presentation
      京都大学
    • Year and Date
      2013-01-12
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] ラフパス理論--反復積分の(確率)解析学--2013

    • Author(s)
      稲浜 譲
    • Organizer
      日本数学会年会 企画講演
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2012

    • Author(s)
      Yuzuru Inahama
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Year and Date
      2012-12-18
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2012

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Oberwolfach workshop 1234b (Rough Path and PDEs) at Mathematisches Forshungsinstitut Oberwolfach
    • Place of Presentation
      Germany
    • Year and Date
      2012-08-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2012

    • Author(s)
      Yuzuru Inahama
    • Organizer
      ラフパス解析とその周辺
    • Place of Presentation
      名古屋大学
    • Year and Date
      2012-01-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2012

    • Author(s)
      稲浜譲
    • Organizer
      ラフパス解析とその周辺
    • Place of Presentation
      名古屋大学(招待講演)
    • Year and Date
      2012-01-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes2012

    • Author(s)
      Yuzuru Inahama
    • Organizer
      Oberwolfach workshop 1234b (Rough Path and PDEs)
    • Place of Presentation
      Mathematisches Forshungsinstitut Oberwolfach
    • Related Report
      2012 Annual Research Report
  • [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
    • Year and Date
      2011-11-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Short time kernel asymptotics for Young SDE driven by fractional Brownian motion by means of Watanabe distribution theory2011

    • Author(s)
      稲浜譲
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      佐賀大学(招待講演)
    • Year and Date
      2011-11-12
    • Related Report
      2011 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 at Senri Life Center
    • Place of Presentation
      Osaka
    • Year and Date
      2010-09-09
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Laplace-type asymptotics for rough differential equation driven by fractional Brownian motion2010

    • Author(s)
      Inahama, Y.
    • Organizer
      34^<th> conference on stochastic processes and its applications
    • Place of Presentation
      大阪千里ライフセンター
    • Year and Date
      2010-09-09
    • 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 at Indian Institute of Statistics
    • Place of Presentation
      Bangalore
    • Year and Date
      2010-08-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Laplace-type asymptotics for rough differential equation driven by fractional Brownian motion2010

    • Author(s)
      Inahama, Y.
    • Organizer
      ICM satellite conference on probability and stochastic processes
    • Place of Presentation
      ISI, Bangalore, India
    • Year and Date
      2010-08-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] ラフパス理論の紹介2010

    • Author(s)
      Yuzuru Inahama
    • Organizer
      城崎新人セミナー
    • Place of Presentation
      城崎地区公民館
    • Year and Date
      2010-02-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Laplace approximation for rough differential equation driven by fractional Brownian motion2009

    • Author(s)
      Yuzuru Inahama
    • 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
      2013 Final Research Report
  • [Presentation] Rough path analysis for an infinite dimensional diffusion2009

    • Author(s)
      Yuzuru Inahama
    • Organizer
      The 1st IMS-APRM (Institute of Mathematical Statistics, Asia-Pacific Rim Meeting)
    • Place of Presentation
      Seuol National University
    • Year and Date
      2009-06-29
    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~inahama/index.html

    • Related Report
      2013 Final Research Report
  • [Remarks] Yuzuru INAHAMA's webpage

    • URL

      http://www.math.nagoya-u.ac.jp/~inahama/index.html

    • Related Report
      2013 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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