Heat kernel estimates for symmetric jump processes with anisotropic jumping kernels

Abstract

We show two-sided bounds of heat kernel for symmetric pure jump Markov process in R d \mathbb {R}^d with jumping kernel J ( x , y ) J(x,y) that is comparable to \frac {\bbone _{\mathcal {V}}(x-y)}{|x-y|^{d+\alpha }}, where V \mathcal {V} is a union of symmetric cones and 0 > α > 2 0>\alpha >2 .