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

Research Project

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
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords確率偏微分方程式 / 確率解析 / 逆問題 / 安定白色雑音 / 量子論 / 統計力学 / 無限次元力学系
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.

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

    (15 results)

All 2013 2012 2011 2010 Other

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (10 results) (of which Invited: 2 results) Remarks (3 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

    • NAID

      120007101150

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [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) Issue: 46 Pages: 465209-465209

    • DOI

      10.1088/1751-8113/44/46/465209

    • NAID

      120007101190

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • 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
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [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
    • Related Report
      2013 Final Research Report
  • [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
    • Related Report
      2013 Final Research Report
  • [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
    • Related Report
      2013 Final Research Report
  • [Presentation] Inverse problems for Stochastic transport equations2011

    • Author(s)
      乙部厳己
    • Organizer
      中央研究院數學研究所 機率研討會
    • Place of Presentation
      Academia Sinica, Taiwan
    • Year and Date
      2011-03-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Recurrent properties for Quantum mechanics2011

    • Author(s)
      乙部厳己
    • Organizer
      中央研究院數學研究所 機率研討會
    • Place of Presentation
      Academia Sinica, Taiwan
    • Year and Date
      2011-03-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Recurrent Properties for Quantum Mechanics2010

    • Author(s)
      乙部厳己
    • Organizer
      East Midland Stochastic Analysis Seminar
    • Place of Presentation
      University of Warwick
    • Year and Date
      2010-06-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] 関数解析的観点による確率(偏)微分方程式

    • 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
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Inverse Problems for Stochastic Transport Equations

    • Author(s)
      Yoshiki Otobe
    • Organizer
      PDE's with random terms
    • Place of Presentation
      湯沢グランドホテル
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Inverse Problems for Stochastic Transport Equations

    • Author(s)
      Yoshiki Otobe
    • Organizer
      確率論シンポジウム
    • Place of Presentation
      京都大学
    • Related Report
      2012 Annual Research Report
  • [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

    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2010 Annual Research Report

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Published: 2010-11-30   Modified: 2019-07-29  

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