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Sample path analysis for symmetric Markov processes and Dirichlet forms

Research Project

Project/Area Number 26400135
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Shiozawa Yuichi  岡山大学, 自然科学研究科, 准教授 (60454518)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords対称マルコフ過程 / ディリクレ形式 / レート関数 / 保存性 / 非再帰性 / 分枝ブラウン運動 / マルコフ過程 / ブラウン運動 / 再帰性 / 脱出レート
Outline of Final Research Achievements

We developed the sample path analysis for symmetric Markov processes generated by regular Dirichlet forms. We first gave estimates on the speed of particles escaping to infinity (lower escape rate) under the condition on the volume growth or heat kernel. We further proved that some integral in the estimates above expresses the decay rate of some tail probability related to the lower escape rate. We next determined the escape rate of the Brownian motions on hyperbolic spaces. We finally proved that for branching Brownian motions on the Euclidean space, the spread rate is determined by the principal eigenvalue of some Schro"dinger type operator under some suitable condition.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (25 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 1 results,  Acknowledgement Compliant: 2 results) Presentation (20 results) (of which Int'l Joint Research: 4 results,  Invited: 14 results) Remarks (2 results)

  • [Int'l Joint Research] 福建師範大学(中国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Escape rate of the Brownian motions on hyperbolic spaces2017

    • Author(s)
      Yuichi Shiozawa
    • Journal Title

      Proceedings of the Japan Academy, Series A, Mathematical Sciences

      Volume: 93 Issue: 4 Pages: 27-29

    • DOI

      10.3792/pjaa.93.27

    • NAID

      40021179824

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Lower Escape Rate of Symmetric Jump-diffusion Processes2016

    • Author(s)
      Yuichi Shiozawa
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 68 Issue: 1 Pages: 129-149

    • DOI

      10.4153/cjm-2015-014-x

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 対称マルコフ過程の大域的性質に関する話題2017

    • Author(s)
      塩沢 裕一
    • Organizer
      岡山―広島 解析・解析セミナー 2017
    • Place of Presentation
      岡山大学
    • Year and Date
      2017-02-20
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Bottom crossing probability for symmetric jump processes2017

    • Author(s)
      塩沢 裕一
    • Organizer
      関西確率論セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2017-01-27
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Bottom crossing probability for symmetric jump processes2016

    • Author(s)
      Yuichi Shiozwa
    • Organizer
      3rd Workshop on Probability Theory and its Applications
    • Place of Presentation
      Korea Institute for Advanced Study (KIAS)
    • Year and Date
      2016-12-13
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Escape rate of the Brownian motions on hyperbolic spaces2016

    • Author(s)
      Yuichi Shiozawa
    • Organizer
      Workshop on Dirichlet Forms and Stochastic Analysis
    • Place of Presentation
      関西大学
    • Year and Date
      2016-11-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Bottom crossing probability for symmetric jump processes2016

    • Author(s)
      塩沢 裕一
    • Organizer
      福岡大学確率論研究集会
    • Place of Presentation
      福岡大学
    • Year and Date
      2016-08-04
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Bottom crossing probability for symmetric jump processes2016

    • Author(s)
      塩沢 裕一
    • Organizer
      Okayama Spring Seminar on Stochastic Analysis
    • Place of Presentation
      岡山大学
    • Year and Date
      2016-03-31
    • Related Report
      2015 Research-status Report
  • [Presentation] 対称マルコフ過程の経路解析に関する話題2016

    • Author(s)
      塩沢 裕一
    • Organizer
      広島・岡山解析確率論セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2016-02-23
    • Related Report
      2015 Research-status Report
  • [Presentation] 対称マルコフ過程の経路解析に関する話題2015

    • Author(s)
      塩沢 裕一
    • Organizer
      静岡確率論セミナー
    • Place of Presentation
      静岡大学
    • Year and Date
      2015-11-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Rate functions for symmetric Markov processes via heat kernel2015

    • Author(s)
      塩沢 裕一
    • Organizer
      関西確率論セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2015-11-06
    • Related Report
      2015 Research-status Report
  • [Presentation] Rate functions for symmetric Markov processes via heat kernel2015

    • Author(s)
      塩沢 裕一
    • Organizer
      関西大学確率論セミナー
    • Place of Presentation
      関西大学システム理工学部
    • Year and Date
      2015-10-24
    • Related Report
      2015 Research-status Report
  • [Presentation] 対称マルコフ過程の大域的性質とディリクレ形式2015

    • Author(s)
      塩沢 裕一
    • Organizer
      日本数学会2015年度秋季総合分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Escape rate of symmetric Markov processes2015

    • Author(s)
      Yuichi Shiozawa
    • Organizer
      国際研究集会 Stochastic Analysis and Applications
    • Place of Presentation
      東北大学さくらホール
    • Year and Date
      2015-09-01
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Quantification of sample path properties of symmetric Markov processes2015

    • Author(s)
      塩沢 裕一
    • Organizer
      RIMS合宿型セミナー 確率解析の新展開
    • Place of Presentation
      国際高等研究所
    • Year and Date
      2015-07-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantification of global properties of symmetric Markov semigroups2015

    • Author(s)
      塩沢 裕一
    • Organizer
      保存則をもつ偏微分方程式に対する解の正則性・特異性の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-06-04
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      塩沢 裕一
    • Organizer
      東北確率論セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2014-11-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      塩沢 裕一
    • Organizer
      関西大学確率論セミナー
    • Place of Presentation
      関西大学(大阪府吹田市)
    • Year and Date
      2014-11-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      Yuichi Shiozawa
    • Organizer
      Workshop on Dirichlet Forms & Stochastic Analysis 2014
    • Place of Presentation
      Technischen Universita"t Dresden(ドイツ・ドレスデン)
    • Year and Date
      2014-10-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      Yuichi Shiozawa
    • Organizer
      Dirichlet Form Theory and its Applications
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach(ドイツ・オーベルヴォルファッハ)
    • Year and Date
      2014-10-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      Yuichi Shiozawa
    • Organizer
      7th International Conference on Stochastic Analysis and its Applications
    • Place of Presentation
      Seoul National University(韓国・ソウル)
    • Year and Date
      2014-08-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Escape rate of symmetric jump-diffusion processes2014

    • Author(s)
      塩沢 裕一
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学(東京都新宿区)
    • Year and Date
      2014-06-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks]

    • URL

      http://www.ems.okayama-u.ac.jp/appl/shiozawa/

    • Related Report
      2015 Research-status Report
  • [Remarks] Yuichi Shiozawa

    • URL

      http://www.ems.okayama-u.ac.jp/appl/shiozawa/

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-02-07  

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