Small-time heat decay for stable processes on fractal drums
ABSTRACT
In this talk, we investigate the heat content associated with isotropic stable processes on fractal drums, that is, open sets with fractal boundaries. While heat content asymptotics on domains with fractal boundaries have been extensively studied for Brownian motions and diffusion processes, much less is known for jump processes. Our aim is to help bridge this gap. We study and compare several notions of heat content for killed subordinate Brownian motions and subordinate killed Brownian motions. We show that their asymptotic behaviors differ at the critical stability index $\alpha=d-\mathfrak{b}$, where $d$ is the dimension of the underlying space and $\mathfrak{b}$ denotes the interior Minkowski dimension of the boundary of the domain. This talk is based on joint work with Y. Xiao.
