Exponential ergodicity for SDEs with jumps and non-Lipschitz coefficients

TL;DR

This paper establishes exponential ergodicity and spectral gap for stochastic differential equations with jumps and non-Lipschitz coefficients by proving irreducibility and the strong Feller property.

Contribution

It demonstrates exponential ergodicity for SDEs with jumps and non-Lipschitz coefficients, extending previous results to more general conditions.

Findings

Proved irreducibility of the transition probabilities.

Established the strong Feller property.

Achieved exponential ergodicity and spectral gap.

Abstract

In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained.