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GEOMETRY OF STOCHASTIC DIFFERENTIAL EQUATIONS

Research Project

Project/Area Number 09044095
Research Category

Grant-in-Aid for international Scientific Research

Allocation TypeSingle-year Grants
SectionJoint Research
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

KUNITA Hiroshi  Kyushu Univ., Grad.Sch.Math., Professor, 大学院数理学研究科, 教授 (30022552)

Co-Investigator(Kenkyū-buntansha) WATANABE Shinzo  Kyoto Univ., Dept.Math., Professor, 大学院理学研究科, 教授 (90025297)
OGURA Yukio  Saga Univ., Dept.Math., Professor, 理工学部, 教授 (00037847)
SUGITA Hiroshi  Kyushu Univ., Grad.Sch.Math., Associate Prof., 大学院数理学研究科, 助教授 (50192125)
TANIGUCHI Setsuo  Kyushu Univ., Grad.Sch.Math., Associate Prof., 大学院数理学研究科, 助教授 (70155208)
SATO Hiroshi  Kyushu Univ., Grad.Sch.Math., Professor, 大学院数理学研究科, 教授 (30037254)
楠岡 成雄  東京大学, 大学院数理科学研究科, 教授 (00114463)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1997: ¥3,600,000 (Direct Cost: ¥3,600,000)
KeywordsStochastic differential equations / Stochstic differential geometry / Stochastic analysis / Malliavin calculus / Harmonic maps / stochastic differeatial equalioes / マリアバン解析 / マリアバン演算 / 調和解析
Research Abstract

In September 1997, including 5 foreign investigators, we gathered together at Kyushu Univ.and discussed various problems concerning stochastic differential equations and stochastic analysis and geometry of infinite dimensional spaces.Also in September 1998, with 3 foreign participants, we discussed stochastic partial differential equations and related analysis. We obtained the following results.
1)Stochastic differential equations on a manifold enable us to define a connect ion on the manifolds. Many proeprties of stochastoic flows can be interpreted through the connection (K.D.Elworthy)
2)We studied an ordinary differential equation with rough path without the Lipschits continuity. It enabled us to apply the stochastic differential equations driven by a Brownian motion. (T.Lyons)
3)Geometry of the loop group. As a typical infinite dimensional group, we studied the loop group which is closely related to the Brownian motion. We discussed the possibility of canstructiong the geometry on the loop group, defining a connection on it. (P.Malliavin)
4)We extend the known L(2) theory of stochastic partial differential equations to that of L(p) theory and obtained a sharper result on the smoothmess of the soluti on. (Krylov)
5)By using anticipating integral (Skorohod integral) and Malliavin calculus, we obtained a new result on the fundamental solution of a stochastic partial differential equation (Nualart)

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] 国田寛: "Infinitesimal genelators of nonhomogeneous convolution semigroups on Lie groups" Osaka Math. J.34. 233-264 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 国田寛: "Infinitesimal genelators of random positive semigroups" Taiwanese J. Math.1. 371-387 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 谷口説男: "Analytic functions Cauchy formula. and stationary phase on a real abstract Wiener space" J.Funct Anal.143・2. 470-528 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 谷口説男: "On the exponential decay of oscillatory integrals on an abstract Wiener space" J.Funct Anal.154. 423-443 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 杉田洋: "Holomorphic Wiener functions" Proc. Taniguchi intern workshop. 399-415 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 杉田洋: "Limit theorem for symmetric statistics with respect to Weyl transformation" 京大紀要. 38・4印刷中. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Kunita: "Infinitesimal generators of nonhomogeneous semigroups on Lie groups" Osaka Math.J.34. 233-264 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Kunita: "Infinitesimal generators of random positive semigroups" Taiwanese J.Math.1. 371-387 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Setsuo Taniguchi: "Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space(with Malliavin, Paul)" J.Funct.Anal.143 No.2. 470-528 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Setsuo Taniguchi: "On the exponential decay of oscillatory integrals on an abstract Wiener space" J.Funct.Anal.154. 424-443 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Sugita: "Holomorphic Wiener Function" New Trends in Stoch.Analysis, Proc.Taniguchi Intern.workshop Charingworth Manor, Sept.21-27,1994 World Scientific. 399-415 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hiroshi Sugita: "Limit theorem for symmetric statistics with respect to Weyl transformation : Disappearance of dependency, with S.Takanobu" Jour.Math.Kyoto Univ.38-4. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 岡田 寛: "Asyaptotic selfsimilarity and short time asymptotics of stechatic flons." 東大紀要. (掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岡田 寛: "Analidicity and injectiovty of donrolution semigroups on Lie groups" J.Funt.Anal.(掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 谷口説男: "On the exponetial decay of osaelatory integrals on an abctract Wienu space" J.Funct.Anal.154. 424-443 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 谷口説男: "On the analytcity of stochartic flowe" Osaha Jour.Marh.(掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 杉田 洋: "Holomurphir Wiever Functions" Proc.Taniguchi Intern.workshop. 399-415 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 杉田 洋: "limit vhedrem for symmatric statistics with respect to Weyl travetionmations." 京大紀要. 38.4(印刷中). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Hiroshi Kunita: "Infinitesimal generators of random positive semigroups" Taiwanese J.Math.1. 371-387 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Kunita: "Asymptptic self similarity and short time asymptotics of stochastic flows" Tokyo Univ.(掲載予定). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Setsuo Taniguchi: "Ahalytic functions,Cauchy formula,and stationary phase or a real abstract Wiener space" J.Funct,Anal.143-2. 470-528 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Setsuo Taniguchi: "On the exponential decay of oscillatory integrals on an abstract Wiener Space" J.Funct.Anal.(掲載予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Sugita: "Holomorphic Wiener Function" New Trends in Stochastic Ahalysis (Proceeding of a Taniguchi). 399-415 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hiroshi Sugita: "Oscillatory integrals with quadratic phase function on a real a bstract Wiener space" J.Funct.Anal.(掲載予定).

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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