Multi-dimensional Brownian motion with darning
by Shuwen Lou
Abstract: For the past few decades, Dirichlet form has been a powerful tool in the study of Markov processes. For example, with the help of Dirichlet form, one may define reflected processes or darning processes in very concise ways. In this talk, first I will introduce the background of the definition of multi-dimensional Brownian motion with darning, which can be intuitively viewed as the random movement of an ant on a ground with a pillar standing vertically on it. Furthermore, using both analytic and probabilistic tools, one can obtain a two-sided heat kernel estimate for this process. This is a joint work with Zhenqing Chen.