Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps

Abstract

We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.

References in corpus (1)

• Non-local Dirichlet Forms and Symmetric Jump Processes

Cited by in corpus (2)

• A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
• Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters