Stochastic analysis of jump-type Markov processes and jump-diffusion processes

• Project/Area Number: 23540172
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kansai University
• Principal Investigator: UEMURA Toshihiro 関西大学, システム理工学部, 教授 (30285332)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: Dirichlet 形式 / マルコフ過程 / 保存性 / ジャンプ拡散過程 / 飛躍型マルコフ過程 / レヴィ過程 / 飛躍型 Dircihlet 形式 / 再帰性

Outline of Final Research Achievements

We succeeded to construct a stochastic process, in particular, a jump-diffusion Markov process by using a lower bounded semi-Dirichlet form theory. Moreover a conservative condition is derived in terms of diffusion data, jump rate and the volume growth of balls with respect to the basic measure. Futher the existence of adjoint Markov process of the jump process is revealed under suitable conditions on the jump kernel.

Research Products

• [Journal Article] On multidimensional diffusion processes with jumps (2014)
  • Author(s): Toshihiro Uemura
  • Journal Title: Osaka Journal of Mathematics Volume: 51 Pages: 969-992
  • NAID: 120005511133
  • Peer Reviewed / Open Access
• [Journal Article] On dual generators for non-local semi-Dirichlet forms (2014)
  • Author(s): Toshihiro Uemura
  • Journal Title: Proabability and Mathematical Statistics Volume: 34 Pages: 199-214
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [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] On the structure of the domain of a symmetric jump type Dirichlet form (2012)
  • Author(s): R. L. Schilling and T. Uemura
  • Journal Title: Publications of the Research Institute for Mathematical Sciences, Kyoto Univ. Volume: 48 Pages: 1-20
  • NAID: 110008904342
  • Peer Reviewed
• [Journal Article] Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms (2012)
  • Author(s): M. Fukushima, and T. Uemura
  • Journal Title: Ann. Probab. Volume: 40 Issue: 2 Pages: 858-889
  • DOI: 10.1214/10-aop633
  • Peer Reviewed
• [Journal Article] On the conservativeness and the recurrence of symmetric jump-diffusions (2012)
  • Author(s): J. Masamune, T. Uemura and J. Wang
  • Journal Title: Journal of Functional Analysis, Volume: 263 Pages: 3984-4008
  • Peer Reviewed
• [Journal Article] $L^p$-Liouville property for nonlocal operators (2011)
  • Author(s): J. Masamune and T. Uemura
  • Journal Title: Mathematische Nachrichten, Volume: 284 Issue: 17-18 Pages: 2249-2267
  • DOI: 10.1002/mana.200910211
  • Peer Reviewed
• [Journal Article] Conservation property of symmetric jump processes (2011)
  • Author(s): J. Masamune and T. Uemura
  • Journal Title: Annales de l’Institut Henri Poincare'- Probabilites et Statistiques, Volume: 47 Issue: 3 Pages: 650-662
  • DOI: 10.1214/09-aihp368
  • Peer Reviewed
• [Presentation] On instabilities of global path properties of symmetric Dirichlet forms under the Mosco convergence (2014)
  • Author(s): Toshihiro Uemura
  • Organizer: Dirichlet Form Theory and its Applications
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2014-10-19 – 2014-10-25
  • Invited
• [Presentation] On a conservativeness of jump-type semi-Dirichlet forms (2014)
  • Author(s): Toshihiro Uemura
  • Organizer: 7th International Conference on Stochastic Analysis and its Applications
  • Place of Presentation: Department of Mathematical Sciences, Seoul National University, South Korea
  • Year and Date: 2014-08-06 – 2014-08-11
  • Invited
• [Presentation] On instability of global properties of symmeric Dirichlet forms under Mosco convergence (2014)
  • Author(s): 鈴木康平，上村稔大
  • Organizer: Stochastic Processes and Mathematical Finance
  • Place of Presentation: 関西大学システム理工学部
• [Presentation] On Recurrence of Symmetric Jump Processes (2013)
  • Author(s): Toshihiro Uemura, Hiroyuki Okura
  • Organizer: Dirichlet Forms and Applications - German-Japanese Meeting on Stochastic Analysis
  • Place of Presentation: Institute of Mathematics, University of Leipzig, Germany
  • Invited
• [Presentation] On instability of global path properties of symmetric Markov processes under Mosco convergence (2013)
  • Author(s): 鈴木康平，上村稔大
  • Organizer: 確率論シンポジウム
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] On dual generators for nonlocal semi-Dirichlet forms (2012)
  • Author(s): T. Uemura
  • Organizer: 6th International Conference on Stochastic Analysis and Its Applications
  • Place of Presentation: Banach Center, Bedlewo, Poland
  • Invited
• [Presentation] 飛躍型 Markov 過程と Dirichlet 形式 (2012)
  • Author(s): 上村稔大
  • Organizer: 日本数学会 2012 秋季総合分科会
  • Place of Presentation: 九州大学，伊都キャンパス
  • Invited
• [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
  • Place of Presentation: 東京理科大学