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The study of asymptotic behavior of Wiener sausages for stochastic processes

Research Project

Project/Area Number 24540181
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKumamoto University

Principal Investigator

Hamana Yuji  熊本大学, 自然科学研究科, 教授 (00243923)

Research Collaborator MATSUMOTO Hiroyuki  
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords確率論 / 確率解析 / ベッセル過程 / 到達時刻 / Wiener sausage / 変形ベッセル関数 / Bessel 過程 / Bessel 関数 / ブラウン運動 / Gegenbauer 多項式 / 歪積表現 / Ornstein-Uhlenbeck 過程 / ベッセル関数
Outline of Final Research Achievements

We give the joint distribution of the hitting time and site of a Brownian motion with and without constant drift. This result yields the formula for the expected volume of the Wiener sausages of Brownian motions and their asymptotic behavior for large time. Moreover we obtain the asymptotics of tail probabilities of first hitting times of Bessel processes with and without the drift. In addition, we find that zeros of Bessel function of the second kind are holomorhic with respect to the indices and establish the method of their calculation with a general-purpose computer soft of computations, Mathematica for example.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 2 results,  Acknowledgement Compliant: 2 results) Presentation (10 results) (of which Invited: 2 results)

  • [Journal Article] ASYMPTOTIC EXPANSION OF THE EXPECTED VOLUME OF THE WIENER SAUSAGE IN EVEN DIMENSIONS2016

    • Author(s)
      Yuji Hamana
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 70 Issue: 1 Pages: 167-196

    • DOI

      10.2206/kyushujm.70.167

    • NAID

      130005152464

    • ISSN
      1340-6116, 1883-2032
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions2016

    • Author(s)
      Yuji Hamana and Hiroyuki Matsumoto
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 未定

    • NAID

      130005433281

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Hitting times to spheres of Brownian motions with and without drifts2016

    • Author(s)
      Yuji Hamana and Hiroyuki Matsumoto
    • Journal Title

      The Proceedings of the American Mathematical Society

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of the probability distributions of the first hitting times of Bessel processes2014

    • Author(s)
      Y.Hamana, H.Matsumoto
    • Journal Title

      Electron. Commun. Probab.

      Volume: 19 Issue: none Pages: 1-5

    • DOI

      10.1214/ecp.v19-3215

    • Related Report
      2013 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The probability distribution of the first hitting time of Bessel processes2013

    • Author(s)
      Yuji Hamana, Hiroyuki Matsumoto
    • Journal Title

      Transaction of teh American Mathematical Society

      Volume: 365 Pages: 5237-5257

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The expected volume and surface area of the Wiener sausage in odd dimensions2012

    • Author(s)
      Yuji Hamana
    • Journal Title

      Osaka Journal of Mathmatics

      Volume: 49 Pages: 83-98

    • NAID

      120005174160

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] The probability densities of the first hitting times of Bessel processes2012

    • Author(s)
      Yuji Hamana, Hiroyuki Hatsumoto
    • Journal Title

      Journal of Math-for-Industry

      Volume: 4B Pages: 91-95

    • NAID

      120005372034

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 定数ドリフトをもつブラウン運動の到達時刻と Wiener sausage について2015

    • Author(s)
      濱名裕治
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Annual Research Report
  • [Presentation] ドリフトをもつブラウン運動の到達時刻と Wiener sausge について2015

    • Author(s)
      濱名裕治
    • Organizer
      研究会「神戸 Workshop 格子上の確率解析とその周辺」
    • Place of Presentation
      神戸大学
    • Year and Date
      2015-03-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Hitting times to spheres of Brownian motion with and without drift2015

    • Author(s)
      濱名裕治・松本裕行
    • Organizer
      新潟確率論ワークショップ
    • Place of Presentation
      新潟大学
    • Year and Date
      2015-01-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Wiener sausage の体積の漸近挙動について2014

    • Author(s)
      濱名裕治
    • Organizer
      日本数学会九州支部例会
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2014-10-25
    • Related Report
      2014 Research-status Report
  • [Presentation] ベッセル過程の到達時刻について

    • Author(s)
      濱名裕治
    • Organizer
      日本数学会九州支部例会
    • Place of Presentation
      宮崎大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ベッセル過程の到達時刻について

    • Author(s)
      濱名裕治
    • Organizer
      共同研究集会「無限分解可能過程に関連する諸問題」
    • Place of Presentation
      統計数理研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Bessel 過程の到達時刻に対する Levy 測度について

    • Author(s)
      濱名裕治
    • Organizer
      研究集会「マルコフ過程とその周辺」
    • Place of Presentation
      東北大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ベッセル過程の到達時刻の挙動について

    • Author(s)
      濱名裕治
    • Organizer
      日本数学会九州支部例会
    • Place of Presentation
      琉球大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ベッセル過程の到達時刻の分布について

    • Author(s)
      濱名裕治,松本裕行
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      福岡市・九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 偶数次元 Wiener sausage の体積の期待値について

    • Author(s)
      濱名裕治,松本裕行
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      福岡市・九州大学
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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