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

2013 Fiscal Year Final Research Report

Stochastic Analytical Study for Mathematical Physics of Statistical Physics and Quantum Theory

Research Project

  • PDF
Project/Area Number 22740086
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionShinshu University

Principal Investigator

OTOBE Yoshiki  信州大学, 理学部, 准教授 (30334882)

Project Period (FY) 2010-10-20 – 2014-03-31
Keywords確率偏微分方程式 / 確率解析
Research Abstract

The aim of the present project was to consider temporal and statial regularities for stochastic partial differential equations of parabolic type driven by stable white noise, and to consider an inverse problem for stochastic linear transport equations. For the first problem, we made an approach by using a theory of complex interpolation spaces, and we discussed the convergence in a specific Banach space which has restricted integrability only. We succeeded in showing the convergence for non-symmetric independent random variables in the space which appears in constructing the solution. For the latter one, we got a nice formula to recover the deterministic coefficients from a random observation using the non-randomness of the quadratic variation process driven by a Gaussian white noise. Also we got several formulae for the problem both additive and multiplicative noise and both the noise was temporal and spatial.

  • Research Products

    (7 results)

All 2013 2012 2011 Other

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (4 results) Remarks (1 results)

  • [Journal Article] Inverse Problems for Stochastic Transport Equations2013

    • Author(s)
      乙部厳己
    • Journal Title

      数理解析研究所講究録

      Volume: 1855 Pages: 140-146

  • [Journal Article] Measure theoretical approach to recurrent properties for quantum dynamics2011

    • Author(s)
      Y. Otobe and I. Sasaki
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 44(46) Pages: 465209(11)

    • DOI

      10.1088/1751-8113/44/46/465209

    • Peer Reviewed
  • [Presentation] 確率偏微分方程式の定式化とその性質2013

    • Author(s)
      乙部厳己
    • Organizer
      愛媛大学解析セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-12-07
  • [Presentation] Inverse Problems for Stochastic Transport Equations2012

    • Author(s)
      乙部厳己
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Year and Date
      2012-12-20
  • [Presentation] Inverse Problems for Stochastic Transport Equations2012

    • Author(s)
      乙部厳己
    • Organizer
      Workshop on PDEs with Random Terms
    • Place of Presentation
      湯沢グランドホテル
    • Year and Date
      2012-06-19
  • [Presentation] 関数解析的視点による確率(偏) 微分方程式2012

    • Author(s)
      乙部厳己
    • Organizer
      サマースクール 『ゆらぎと微分方程式』
    • Place of Presentation
      東京大学
    • Year and Date
      2012-06-16
  • [Remarks] 乙部厳己, 新入生のための数学書ガイド, 日本評論社, 数学セミナー, 2013年(4月号) 2013(Mar. 12)

    • URL

      http://argent.shinshu-u.ac.jp

URL: 

Published: 2015-06-25  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi