Subordinated Markov processes: sharp estimates for heat kernels and Green functions

TL;DR

This paper establishes precise estimates for heat kernels and Green functions of subordinate Markov processes, demonstrating stability in discrete cases under weak assumptions on the original processes and subordinators.

Contribution

It provides sharp bounds for heat kernels and Green functions for subordinate Markov processes, including stability results in discrete settings, under minimal assumptions.

Findings

Sharp estimates for heat kernels and Green functions.

Stability of heat kernel estimates in discrete settings.

Applicable under weak assumptions on processes and subordinators.

Abstract

We prove sharp estimates on heat kernels and Green functions for subordinate Markov processes with both discrete an continuous time, under relatively weak assumptions about original processes as well as Laplace exponents of subordinators. We also show stability of heat kernel estimates in the discrete settings.