Limit theorems of functionals for Markov processes and their applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 23740073
• 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: Kyoto Sangyo University (2012-2015); Kyoto University (2011)
• Principal Investigator: YANO Yuko 京都産業大学, 理学部, 准教授 (10337462)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 確率論 / 確率過程論 / マルコフ過程 / 拡散過程 / 加法過程 / 極限定理 / 一般化逆正弦法則 / 処罰問題

Outline of Final Research Achievements

I studied some limit theorems of functionals for Markov processes and obtained the following results: I studied asymptotic behavior of the law of the occupation time for Brownian motion and random walks on fractals (joint work with N. Kajino et al.); I obtained some remarkable results for the joint law of occupation times for a diffusion process on multiray; I showed the new method to calculate special values of the Hurwitz zeta function via generalized Cauchy variables (joint work with T. Fujita); I succeeded to obtain a sigma-finite measure unifying supremum penalisations for a stable Levy process; I studied h-transforms of one-dimensional diffusions stopped upon hitting zero (joint work with K. Yano); I studied local time penalisations with various random clocks (joint work with C. Profeta et al.).

Free Research Field

確率論