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

2015 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

基礎解析学