Analysis of asymptotic behaviors of Markov processes

• Project/Area Number: 23740078
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• 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): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 確率論 / 対称マルコフ過程 / ディリクレ形式 / 保存性 / 脱出レート / Silverstein 拡大 / Silverstein 拡大 / マルコフ過程 / Escape rate / 飛躍拡散型マルコフ過程 / Silverstein 拡張

Research Abstract

Conservativeness criteria and upper estimates of the escape rate are established for symmetric jump-diffusion processes generated by regular Dirichlet forms. Furthermore, these results are proved to be sharp by using concrete examples. It is also prove that the Silverstein extension of a regular Dirichlet form is unique under some topological property of the associated intrinsic metric.

Research Products

• [Journal Article] Explosion of jump-type symmetric Dirichlet forms on Rd (2014)
  • Author(s): Yuichi Shiozawa, Toshihiro Uemura
  • Journal Title: Journal of Theoretical Probability Volume: 27 Pages: 402-432
  • Peer Reviewed
• [Journal Article] Upper escape rate of Markov chains on weighted graphs (2014)
  • Author(s): X. Huang, 塩沢裕一
  • Journal Title: Stochastic Process. Appl Volume: 124 Issue: 1 Pages: 317-347
  • DOI: 10.1016/j.spa.2013.08.004
  • Peer Reviewed
• [Journal Article] Conservation property of symmetric jump-diffusion processes (2012)
  • Author(s): Yuichi Shiozawa
  • Journal Title: Forum Mathematicum Volume: (掲載予定) Issue: 1 Pages: 519-548
  • DOI: 10.1515/forum-2012-0043
  • Year and Date: 2012-12-14
  • Peer Reviewed
• [Journal Article] Explosion of jump-type symmetric Dirichlet form on R^d (2012)
  • Author(s): 塩沢裕一, 上村捻大
  • Journal Title: J. Theoretical Probability Volume: 27 Issue: 2 Pages: 1-29
  • DOI: 10.1007/s10959-012-0424-5
  • Peer Reviewed / Open Access
• [Journal Article] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms
  • Author(s): Kazuhiro Kuwae, Yuichi Shiozawa
  • Journal Title: Mathematische Nachrichten Volume: (掲載決定)
  • Peer Reviewed
• [Presentation] Escape rate of symmetricjump-diffusion processes (2014)
  • Author(s): 塩沢裕一
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Year and Date: 2014-02-01
• [Presentation] Escape rate of symmetric Markov processes (2013)
  • Author(s): 塩沢裕一
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学
  • Year and Date: 2013-12-19
• [Presentation] Upper escape rate of Markovchains on weighted graphs (2013)
  • Author(s): 塩沢裕一
  • Organizer: 東京確率論セミナー
  • Place of Presentation: 東京工業大学
  • Year and Date: 2013-11-18
• [Presentation] Upper escape rate of Markovchains on weighted graphs (2013)
  • Author(s): 塩沢裕一
  • Organizer: 確率解析とその周辺
  • Place of Presentation: 京都大学
  • Year and Date: 2013-09-20
• [Presentation] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms (2013)
  • Author(s): Yuichi Shiozawa
  • Organizer: Workshop on Geometric aspects in probability and analysis
  • Place of Presentation: Friedrich Schiller Universitat Jena
  • Year and Date: 2013-09-14
• [Presentation] Upper escape rate of Markov chains on weighted graphs (2013)
  • Author(s): Yuichi Shiozawa
  • Organizer: Dirichlet Forms and Applications German-Japanese Meeting on Stochastic Analysis
  • Place of Presentation: Universitat Leipzig
  • Year and Date: 2013-09-10
• [Presentation] 対称マルコフ過程の大域的性質に関する話題 (2013)
  • Author(s): 塩沢裕一
  • Organizer: 確率論早春セミナー
  • Place of Presentation: 関西大学
  • Year and Date: 2013-03-17
• [Presentation] 対称マルコフ過程の長時間挙動の解析 (2012)
  • Author(s): 塩沢裕一
  • Organizer: 長岡解析確率論セミナー
  • Place of Presentation: 長岡工業高等専門学校
  • Year and Date: 2012-10-26
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • Author(s): Yuichi Shiozawa
  • Organizer: 6th International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: Conference Center in Bedlew
  • Year and Date: 2012-09-11
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • 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: 2012-07-20
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • Author(s): Yuichi Shiozawa
  • Organizer: Nonlocal Operators : Analysis,Probability, Geometry and Applications
  • Place of Presentation: ZiF Bielefeld
  • Year and Date: 2012-07-13
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • 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: 2012-05-18
• [Presentation] Explosion of jump-type symmetric Dirichlet forms on Rd (2012)
  • Author(s): 上村稔大 ,塩沢裕一
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-26
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • Author(s): Yuichi Shiozawa
  • Organizer: Stochastic Analysis and its Applications
  • Place of Presentation: 新潟大学ときめいと
  • Year and Date: 2012-03-16
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • 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: 2012-02-11
• [Presentation] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms (2012)
  • Author(s): 塩沢裕一
  • Organizer: 非正則な拡散過程における諸問題
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2012-01-29
• [Presentation] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet form (2012)
  • Author(s): 塩沢裕一
  • Organizer: 非正則な拡散過程における諸問題
  • Place of Presentation: 奈良女子大学
• [Presentation] Conservation property of symmetric jump-diffusion processes (2012)
  • 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
• [Presentation] Explosion of jump-type symmetric Dirichlet forms on ${\mathbb R}^d$ (2012)
  • Author(s): 上村稔大，塩沢裕一
  • Organizer: 日本数学会２０１２年度年会
  • Place of Presentation: 東京理科大学
• [Presentation] Rd上の対称マルコフ過程の保存性について (2011)
  • 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: 2011-12-09
• [Presentation] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms (2011)
  • Author(s): 塩沢裕一
  • Organizer: 確率解析とその周辺
  • Place of Presentation: 佐賀大学
  • Year and Date: 2011-11-11
• [Presentation] ${\mathbb R}^d$ 上の対称マルコフ過程の保存性について (2011)
  • Author(s): 塩沢裕一
  • Organizer: 東北確率論セミナー
  • Place of Presentation: 東北大学
• [Presentation] Upper escape rate of Markov chains on weighted graphs
  • Author(s): Yuichi Shiozawa
  • Organizer: Dirichlet Forms and Applications German-Japanese Meeting on Stochastic Analysis
  • Place of Presentation: ライプチヒ大学，ドイツ
  • Invited
• [Presentation] A remark on the uniqueness of Silverstein extensions of symmetric Dirichlet forms
  • Author(s): Yuichi Shiozawa
  • Organizer: Workshop on Geometric aspects in probability and analysis
  • Place of Presentation: イェーナ大学，ドイツ
• [Presentation] Upper escape rate of Markov chains on weighted graphs
  • Author(s): 塩沢 裕一
  • Organizer: 確率解析とその周辺
  • Place of Presentation: 京都大学
• [Presentation] Upper escape rate of Markov chains on weighted graphs
  • Author(s): 塩沢 裕一
  • Organizer: 東京確率論セミナー
  • Place of Presentation: 東京工業大学
• [Presentation] Escape rate of symmetric Markov processes
  • Author(s): 塩沢 裕一
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学
• [Presentation] Escape rate of symmetric jump-diffusion processes
  • Author(s): 塩沢 裕一
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Invited
• [Presentation] Conservation property of symmetric jump-diffusion processes
  • Author(s): 塩沢 裕一
  • Organizer: 関西確率論セミナー
  • Place of Presentation: 京都大学
• [Presentation] Conservation property of symmetric jump-diffusion processes
  • Author(s): Yuichi Shiozawa
  • Organizer: Nonlocal Operators: Analysis, Probability, Geometry and Applications
  • Place of Presentation: ZiF Bielefeld，ドイツ連邦共和国
• [Presentation] Conservation property of symmetric jump-diffusion processes
  • Author(s): 塩沢 裕一
  • Organizer: 東北確率論セミナー
  • Place of Presentation: 東北大学
• [Presentation] Conservation property of symmetric jump-diffusion processes
  • Author(s): Yuichi Shiozawa
  • Organizer: 6th International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: Conference Center in Bedlewo，ポーランド共和国
• [Presentation] 対称マルコフ過程の長時間挙動の解析
  • Author(s): 塩沢 裕一
  • Organizer: 長岡解析・確率論セミナー
  • Place of Presentation: 長岡工業高等専門学校
• [Presentation] 対称マルコフ過程の大域的性質に関する話題
  • Author(s): 塩沢 裕一
  • Organizer: 確率論早春セミナー
  • Place of Presentation: 関西大学
• [Remarks]
  • URL: http://www.ems.okayama-u.ac.jp/appl/shiozawa/
• [Remarks] Yuichi Shiozawa
  • URL: http://www.ems.okayama-u.ac.jp/appl/shiozawa/