Ergodicity of L\'evy-Type Processes

TL;DR

This paper establishes conditions under which Levy-type Feller processes exhibit ergodic behavior, including transience, recurrence, and various forms of ergodicity, based on their generator coefficients, and discusses their mixing properties.

Contribution

It provides new criteria linking generator coefficients to ergodic properties of Levy-type processes, enhancing understanding of their long-term behavior.

Findings

Conditions for transience and recurrence are derived.

Criteria for strong, subexponential, and exponential ergodicity are established.

Mixing properties of Levy-type processes are analyzed.

Abstract

In this paper, conditions for transience, recurrence, ergodicity and strong, subexponential (polynomial) and exponential ergodicity of a class of Feller processes are derived. The conditions are given in terms of the coefficients of the corresponding infinitesimal generator. As a consequence, mixing properties of these processes are also discussed.