Heat kernels for non-symmetric diffusion operators with jumps

Abstract

For $d\ge 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators non-divergence form and a non-local $\alpha$-stable-type operator with bounded time-dependent coefficient. Moreover, we obtain sharp two-sided estimates, gradient estimate and fractional derivative estimate for the heat kernels under some mild conditions. Our approach is mainly analytic but also uses some probabilistic techniques.

42 pages

Cited by in corpus (2)

• Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel
• Stability of Heat Kernel Estimates for Diffusions with Jumps under Non-local Feynman-Kac Perturbations