• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Stochastic analysis and stochastic control for symmetric Markov processes

Research Project

Project/Area Number 11640142
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKANSAI UNIVERSITY

Principal Investigator

FUKUSHIMA Masatoshi  Kansai Univ., Faculty of Engineering, Prof., 工学部, 教授 (90015503)

Co-Investigator(Kenkyū-buntansha) YAMAMOTO Noboru  Kansai Univ. Faculty of Engineering. Prof., 工学部, 教授 (80029628)
ISII Keiiti  Kansai Univ. Faculty of Engineering, Prof., 工学部, 教授 (80029420)
KURISU Tadashi  Kansai Univ. Faculty of Engineering, Prof., 工学部, 教授 (00029159)
MAEDA Toru  Kansai Univ. Faculty of Engineering, Associate Prof., 工学部, 助教授 (20199623)
HIRASHIMA Yasumasa  Kansai Univ. Faculty of Engineering. Associate Prof., 工学部, 助教授 (80047399)
楠田 雅治  関西大学, 工学部, 助教授 (80195437)
柳川 高明  関西大学, 工学部, 教授 (00031310)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordssymmetic Markov processes / Dirichlet forms / stochastic analysis / stochastic control / semi-martingale / Ito's formula / BV functions / stochastic games / ディリクレ形式 / 確率特異制御理論 / マルコフ過程 / 半マルティンゲール / ガウスの公式 / 抽象ウィーナー空間 / BV関数 / 特異確率制御
Research Abstract

For a general symmetric Markov process X(t) and a function u in the associated quasi-regular Dirichlet space, the head investigator succeeded to give a quite useful necessary and sufficient conditions for the composite process u(X(t)) to be a semimartingale.
Then he cooperates with other investigators to apply the above mentioned general criteria first for symmetric diffusion processes in finite dimensions to identify necessary and sufficient smoothness for a function to make Ito's formula invariant. Second, finite dimensional notions of BV functions are extended to the infinite dimensional abstract Wiener space and the associated Gauss formula and the Skorohod 1 equations are exploited. The head investigator also has written a joint paper on a singular control problem with Professor Taksar by extending a previous paper by Taksar considerably, combining it with a Nagai-Zabczyk characterization of a stochastic zero sum game by a Dirichelt form.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] M.Fukushima: "On semi-martingale characterizations of functionals of symmetric Markov processes"Electronic Journal of Probability. 4no.18. 1-32 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "On It's formulae for additive functionals of symmetric diffusion processes"Canadian Mathematical Society Conference Proceedings. 28. 201-211 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space"Journal of Functional Analysis. 174. 227-249 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima and M.Hino: "On the space of BV functions and a related stochastic caloulus in infinite dimensions"Journal of Functional Analysis. (in Press). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "On semi-martingale characterizations of functionals of symmetric Markov processes"Electronic Journal of Probability, 4, page. no.18. 1-32 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "On Ito's formulae for additive functionals of symmetic diffusion processes"Canadian Math.Soc.Conf.Proc.. 28. 201-211 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space"Journal of Functional Analysis. 174. 227-249 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "On the space of BV functions and a related stochastic calculus in infinite dimensions"Journal of Functional Analysis. (in Press). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Fukushima: "BV functions and distorted Ornstein Uhlenbeck processes ouer the alstract Wiener space"Journal of Functional Analysis. 174. 227-249 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Fukushima: "On Ito's for mulae for additive functionals of symmetnic diffusion processes"Canadian Mathematical Society Conference Proceedings. 28. 201-211 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Fukushima and M.Hine: "On the space of BV functions and a related stochastic calculus in infinite dimensions"Journal of Functional Analysis. (in press). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] M. Fukushima, T. Shima, M. Takeda: "Large deviations and related LIL's for Brownian motions on nested fractals"Osaka Journal of Mathematics. 36. 497-537 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Fukushima: "On semimartingale characterigations of functionals of symmetric Markou processes"Electronic Journal of Probability. 4, no18. 1-32 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Fukushima: "On Ito's formulae for additive functionals of symmetric diffusion processes"Canadian Math, Soc, Conference Proc,. (印刷中).

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Fukushima: "BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space"Journal of Functional Analysis. (印刷中).

    • Related Report
      1999 Annual Research Report

URL: 

Published: 1999-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi