Stochastic analysis based on Feynman-Kac functionals and its applications to potential theory

• Project/Area Number: 24740093
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Nagaoka National College of Technology
• Principal Investigator: Tawara Yoshihiro 長岡工業高等専門学校, 一般教育科, 准教授 (00567901)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: ファインマン・カッツ汎関数 / 大偏差原理 / ディリクレ形式 / 対称マルコフ過程 / マルコフ過程 / 確率解析

Outline of Final Research Achievements

We studied asymptotic behaviors of symmetric Feynman-Kac functionals of various Markov processes. In particular, we show the large deviation principle for positive continuous additive functionals of nealry stable processes. Moreover, we show large deviation principles for the occupation distribution of a symmetric Markov process normalized by Feynman-Kac functional under the conditions for the Markov processes to be Feller, strong Feller and tight. Moreover, we proved the generalized Fukushima's decomposition.

Research Products

• [Journal Article] Large deviation principles for generalized Feynman-Kac functionals and its applications (2016)
  • Author(s): Daehong Kim, Kazuhiro Kuwae and Yoshihiro Tawara
  • Journal Title: Tohoku Mathematical Journal
  • NAID: 130008106073
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Differentiability of Spectral Functions for Nearly Stable Processes and Large Deviations (2014)
  • Author(s): Yoshihiro Tawara and Kaneharu Tsuchida
  • Journal Title: Infinite Dimensional Analysis, Quantum Probability and Related Topics Volume: 17 Issue: 03 Pages: 1450017-1450017
  • DOI: 10.1142/s0219025714500179
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A Large Deviation Principle for Symmetric Markov Processes Normalized by Feynman-Kac Functionals (2013)
  • Author(s): M. Takeda and Y. Tawara
  • Journal Title: Osaka Journal of Mathematics Volume: 50 Pages: 287-307
  • NAID: 120005294078
  • Peer Reviewed
• [Presentation] On an extension of Persson's theorem (2015)
  • Author(s): Yoshihiro Tawara
  • Organizer: Summer School on Dirichlet Forms and Stochastic Analysis, Young Forum
  • Place of Presentation: 関西大学(大阪府吹田市)
  • Year and Date: 2015-08-26
  • Int'l Joint Research
• [Presentation] シュレディンガー型作用素のスペクトル下限のL^p独立性とそれに関する話題, (2014)
  • Author(s): 田原喜宏
  • Organizer: 函数論シンポジウム
  • Place of Presentation: 東北大学AIMR(宮城県仙台市)
  • Year and Date: 2014-11-08
  • Invited
• [Presentation] A Large Deviation Principle for Symmetric Markov Processes Normalized by Feynman-Kac Functionals (2013)
  • Author(s): 田原喜宏
  • Organizer: マルコフ過程とその周辺
  • Place of Presentation: 東北大学
• [Remarks] Tawara Yoshihiro's Web page
  • URL: http://www.nagaoka-ct.ac.jp/~tawara/
• [Remarks] TAWARA Yoshihiro's Web Page
  • URL: http://www.nagaoka-ct.ac.jp/~tawara/
• [Remarks] TAWARA Yoshihro's Web Page
  • URL: http://www.nagaoka-ct.ac.jp/~tawara/
• [Remarks] Read & Researchmap
  • URL: http://researchmap.jp/yoshihiro_tawara/