Abstract

Starting with a transient irreducible diffusion process on a locally compact separable metric space (for example, absorbing Brownian motion in a snowflake domain), one can construct a canonical symmetric reflected diffusion process on a completion of through the theory of reflected Dirichlet spaces. The boundary trace process of on the boundary is the reflected diffusion process time-changed by a smooth measure having full quasi-support on , which is unique up to a time change. The Dirichlet form of the trace process is called the trace Dirichlet form. In this talk, I will address the following two fundamental questions:

1) How to characterize the boundary trace Dirichlet space in a concrete way?

2) How does the boundary trace process behave?

Based on a joint work with Shiping Cao.

 

Organizer: Shuenn-Jyi Sheu (NCCU)