Global properties and the theory of convergences of diffusion processes of measure spaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400062
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University (2016-2017); Tohoku University (2014-2015)
• Principal Investigator: Masamune Jun 北海道大学, 理学研究院, 教授 (50706538)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 保存則 / 再帰性 / リュービル性 / ディリクレ形式 / 本質的自己共役性

Outline of Final Research Achievements

In this research project, we aim to develop the global analysis of diffusion processes on measure spaces associated with some Markov processes. The main results in this projects are (1) conservation property and recurrence of general Markov processes in terms of Green's formula (2) Characterizations of Liouville type problems of Riemannian manifolds and graphs (3) Generalized conservation property of Brownian motion with killing inside and its characterizations (4) Probabilisitic characterization of the essential selfadjointness of the Laplacian of Euclidean space removed a compact set.

Free Research Field

幾何学