Title: Stability of heat kernel estimates for non-local operators with diffusion under the Feynman-Kac perturbation

Speaker: Kyoung-Youn Kim (National Chung Hsing University)

Title: Stability of heat kernel estimates for non-local operators with diffusion under the Feynman-Kac perturbation

Abstract: Let $X_t$ be a symmetric jump-type process with a diffusion and $\{P_t\}_{t\geq 0}$ be  its transition semigroup .
The Feynman-Kac semigroup of $X$ is given by
$$T_t f(x)={\bf E}_x[\exp(A_t) f(X_t)], \qquad t\ge 0, x\in M$$
where $A_t$ is a non-local additive functional of $X_t$.
We introduce a Kato condition to obtain the heat kernel estimates for the FK-semigroup and obtain the stability of heat kernels under the FK-perturbation.
Also we discuss the parabolic Harnack principle of the FK-semigroup.
This is joint work with Zhen-Qing Chen and Lidan Wang.