Stochastic analysis of Markov processes in terms of Dirichlet forms

• Project/Area Number: 20540130
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: University of Hyogo
• Principal Investigator: UEMURA Toshihiro University of Hyogo, システム理工学部, 教授 (30285332)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: ディリクレ形式 / 飛躍型マルコフ過程 / フェラー半群 / 対称マルコフ過程 / ジャンプ型確率過程 / 保存性 / 非局所型作用素 / マルコフ連鎖の収束 / フェラー性 / マルコフ過程 / 平行場作用素 / ハルナック不等式 / 脱出時刻 / 安定型過程 / ジャンプ過程

Research Abstract

We succeeded to construct a stochastic process, namely, a jump-type Markov process, for which is known as a mathematical model of"unknown phenomena", by using a symmetric Dirichlet form theory. Moreover an exact form of the infinitesimal generator is given and some global path properties also are obtained; the conservativeness and the mean of the exit time from a ball.

Research Products

• [Journal Article] Convergence of symmetric Markov chains on Z^d (2010)
  • Author(s): Richard F.Bass, Takashi Kumagai, Toshihiro Uemura
  • Journal Title: Probability Theory and Related Fields vol.148 Pages: 107-140
  • Peer Reviewed
• [Journal Article] Perturbation approach to the Feller property for non-local operators (2010)
  • Author(s): Yuichi Shiozawa, Toshihiro Uemura
  • Journal Title: RIMS Kokyuroku vol.1672 Pages: 131-142
• [Journal Article] Stability of Feller property for non-local operators by bounded perturbations (2010)
  • Author(s): Yuichi Shioazawa, Toshihiro Uemura
  • Journal Title: Glasnik Matematickis vol.45 Pages: 155-172
  • Peer Reviewed
• [Journal Article] On exit time from balls of jump-type symmetric Markov processes (2010)
  • Author(s): Toshihiro Uemura
  • Journal Title: Acta Mathematica Sinica, English Series vol.26 Pages: 185-192
  • Peer Reviewed
• [Journal Article] On exit time from balls of jump-type symmetric Markov processes (2010)
  • Author(s): T.Uemura
  • Journal Title: Acta Math.Sinica, English Series Volume: 26 Pages: 185-192
  • Peer Reviewed
• [Journal Article] Stability of Feller property for non-local operators by bounded perturbations (2010)
  • Author(s): Y.Shiozawa T.Uemura
  • Journal Title: Glasnik Matematicki Volume: 45 Pages: 155-172
  • Peer Reviewed
• [Journal Article] Convergence of symmetric Markov chains on Z^d (2010)
  • Author(s): R.Bass, T.Kumagai T.Uemura
  • Journal Title: Probab.Theory and Related Fields Volume: 148 Pages: 107-140
  • Peer Reviewed
• [Journal Article] On exit time from balls of jump-type symmetric Markov processes (2010)
  • Author(s): T.Uemura
  • Journal Title: Acta Mathematica Sinica, English Series 26 Pages: 185-192
  • Peer Reviewed
• [Journal Article] A remark on non-local operators with variable order (2009)
  • Author(s): Toshihiro Uemura
  • Journal Title: Osaka Journal of Mathematics vol.46 Pages: 503-514
  • NAID: 120005986667
  • Peer Reviewed
• [Journal Article] A remark on non-local operators with variable order (2009)
  • Author(s): T.Uemura
  • Journal Title: Osaka Journal of Mathematics 46 Pages: 503-514
  • NAID: 120005986667
  • Peer Reviewed
• [Journal Article] A remark on non-local operators with variable order (2009)
  • Author(s): 上村稔大
  • Journal Title: Osaka Journal of Mathematics 46(to appear)
  • NAID: 120005986667
  • Peer Reviewed
• [Presentation] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms (2010)
  • Author(s): 上村稔大
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-22
• [Presentation] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms (joint work with M. Fukushima) (2010)
  • Author(s): T.Uemura
  • Organizer: 平成22年度 確率論シンポジウム
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2010-12-22
• [Presentation] On integro-differential operators : Conservativeness and the Feller Property (2010)
  • Author(s): 塩沢裕一,上村稔大
  • Organizer: 日本数学会,秋季総合分科会,統計分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] On integro-differential operators : Conservativeness and the Feller property (2010)
  • Author(s): 塩沢裕一, 上村稔大
  • Organizer: 日本数学会 秋季総合分科会 統計数学分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Conservation property of symmetric jump processes (2009)
  • Author(s): Toshihiro Uemura
  • Organizer: Fine properties of stochastic processes
  • Place of Presentation: ビーレフェルド大学,ドイツ
  • Year and Date: 2009-11-30
• [Presentation] On the structure of the domain of a symmetric jump type Dirichlet form (2009)
  • Author(s): 上村稔大
  • Organizer: マルコフ過程と確率解析
  • Place of Presentation: 岡山大学
• [Presentation] On the structure Of the domain of a symmetric jump-type Dirichlet forms (2009)
  • Author(s): Toshihiro Uemura
  • Organizer: Conference on Stochastic Differential Equations and Related Topics
  • Place of Presentation: マンチェスター大学,イギリス
• [Presentation] Consevation property of symmetric jump processes (2008)
  • Author(s): Toshihiro Uemura
  • Organizer: International Workshop on Probability and Its Applications
  • Place of Presentation: 国立ソウル大学,韓国
  • Year and Date: 2008-12-12
• [Presentation] Derivation property and L^p-Liouville property for non-local operator (2008)
  • Author(s): Toshihiro Uemura
  • Organizer: 2^<nd> International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: 国立ソウル大学,韓国
• [Presentation] Convergence of symmetric diffusion processes with jumps (2000)
  • Author(s): Toshihiro Uemura
  • Organizer: 3^<rd> International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: 北京理工大学,中国