Approximation of Stable-dominated Semigroups

TL;DR

This paper studies Feller semigroups influenced by stable Lévy measures, providing an approximation method to establish their existence and derive heat kernel estimates.

Contribution

It introduces an approximation scheme for stable-dominated semigroups, proving their existence and estimating heat kernels.

Findings

Established existence of stable-dominated Feller semigroups.

Derived heat kernel estimates for these semigroups.

Provided a new approximation approach for jump processes.

Abstract

We consider Feller semigroups of operators determinated by systems of jumps dominated by the rotation invariant stable L\'evy measure. Using an approximation schema we prove the existence and obtain estimates of corresponding heat kernels.