Sample path analysis for symmetric Markov processes and Dirichlet forms

• Project/Area Number: 26400135
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Okayama 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: ¥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.

Research Products

• [Int'l Joint Research] 福建師範大学(中国)
• [Journal Article] Escape rate of the Brownian motions on hyperbolic spaces (2017)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Lower Escape Rate of Symmetric Jump-diffusion Processes (2016)
  • Author(s): Yuichi Shiozawa
  • Journal Title: Canadian Journal of Mathematics Volume: 68 Issue: 1 Pages: 129-149
  • DOI: 10.4153/cjm-2015-014-x
  • 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
  • Invited
• [Presentation] Bottom crossing probability for symmetric jump processes (2017)
  • 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
  • Invited
• [Presentation] Bottom crossing probability for symmetric jump processes (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Escape rate of the Brownian motions on hyperbolic spaces (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Bottom crossing probability for symmetric jump processes (2016)
  • 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
  • Invited
• [Presentation] Bottom crossing probability for symmetric jump processes (2016)
  • 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
• [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
• [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
• [Presentation] Rate functions for symmetric Markov processes via heat kernel (2015)
  • 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
• [Presentation] Rate functions for symmetric Markov processes via heat kernel (2015)
  • 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
• [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
  • Invited
• [Presentation] Escape rate of symmetric Markov processes (2015)
  • 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
  • Int'l Joint Research
• [Presentation] Quantification of sample path properties of symmetric Markov processes (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Quantification of global properties of symmetric Markov semigroups (2015)
  • 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
  • Invited
• [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Presentation] A note on the lower escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Presentation] Escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Presentation] Escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Presentation] Escape rate of symmetric jump-diffusion processes (2014)
  • 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
  • Invited
• [Remarks]
  • URL: http://www.ems.okayama-u.ac.jp/appl/shiozawa/
• [Remarks] Yuichi Shiozawa
  • URL: http://www.ems.okayama-u.ac.jp/appl/shiozawa/