DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Hyunchul Park (State University of New York at New Paltz)

Title: Small-time behavior of the spectral heat content for isotropic Levy processes

Abstract: The spectral heat content (SHC) measures the total heat that remains on a domain when the initial temperature is one and the outside temperature is identically zero. When one replaces the Laplace operator in the heat equation with generators of Levy processes, one obtains SHC for those Levy processes. Recently, the two-term asymptotic behavior of SHC for isotropic stable processes on bounded \(C^{1,1}\) open sets were investigated by Park and Song (EJP 2022). In this talk, we generalize their result to cover Levy processes with regularly varying characteristic exponent with index in (1,2]. The proof provides a unified approach to the study of SHC and is applicable to both Brownian motions and jump processes.

This is a joint work with Kei Kobayashi (Fordham University).