Heat kernel estimates for anisotropic symmetric jump processes

Abstract

We show two-sided bounds of heat kernel for anisotropic non-singular symmetric pure jump Markov process whose jump kernel $J(x,y)$ is comparable to $\frac{1_{\mathcal{V}}(x-y)}{|x-y{|}^{d+\alpha }}$, where $\mathcal{V}$ is a union of symmetric cones, $0<\alpha <2$ and $x,y\in {\mathbb{R}}^d$.

17 pages