时间：2013年06月04日（周二）15:30-16:30
地点：旗山校区理工楼统计实验室109
主讲：Professor Dr. Jun Masamune, Tohoku University, Japan
主办：数学与计算机科学学院
专家简介：Jun Masamune教授，其主要研究方向包括：微分几何、分形几何和随机分析。已在《Comm. in Partial Diff. Equations》， 《Journal de Math. Pures et Appli.》 《J. Funct. Anal.》《Math、Z.》重要期刊上发表学术论文近20篇。
报告摘要：We present and prove new characterizations of recurrence and stochastic completeness of Markov processes generated by Dirichlet forms in terms of generalized Green’s formula. Recently it has been shown by several researchers that a wide class of Markov processes on a measure space is recurrent and stochastic complete provided that the space is not "too large" at infinity. On the other hand, these properties of Brownian motion on a weighted Riemannian manifold were characterized in terms of Green's formula by A. Grigoryan and the author in 2013. In this talk, we will extend this result to a very general situation by developing and applying new techniques in the theory of Dirichlet forms. The result was obtained in a collaborative effort with S. Haeseler, M. Keller, D. Lenz, and M. Schumidt (Jena,Germany).