Sample path analysis for symmetric Markov processes and Dirichlet forms

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400135
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Okayama University
• Principal Investigator: Shiozawa Yuichi 岡山大学, 自然科学研究科, 准教授 (60454518)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 対称マルコフ過程 / ディリクレ形式 / レート関数 / 保存性 / 非再帰性 / 分枝ブラウン運動

Outline of Final Research Achievements

We developed the sample path analysis for symmetric Markov processes generated by regular Dirichlet forms. We first gave estimates on the speed of particles escaping to infinity (lower escape rate) under the condition on the volume growth or heat kernel. We further proved that some integral in the estimates above expresses the decay rate of some tail probability related to the lower escape rate. We next determined the escape rate of the Brownian motions on hyperbolic spaces. We finally proved that for branching Brownian motions on the Euclidean space, the spread rate is determined by the principal eigenvalue of some Schro"dinger type operator under some suitable condition.

Free Research Field

確率過程論