The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm

TL;DR

This paper proves a version of the central limit theorem for certain Markov processes that are exponentially ergodic in the bounded-Lipschitz norm, extending CLT applicability to a broader class of stochastic processes.

Contribution

It establishes a CLT for Markov-Feller processes with exponential ergodicity in the bounded-Lipschitz norm under a continuous Foster-Lyapunov condition, including specific PDMP examples.

Findings

Proves CLT for Markov processes with exponential ergodicity in bounded-Lipschitz norm.

Verifies assumptions for a class of piecewise-deterministic Markov processes.

Extends CLT applicability to processes with continuous semiflows and random switching.

Abstract

In this paper, we establish a version of the central limit theorem for Markov-Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bounded-Lipschitz distance and enjoy a continuous form of the Foster-Lyapunov condition. As an example, we verify the assumptions of our main result for a specific piecewise-deterministic Markov process, whose deterministic component evolves according to continuous semiflows, switched randomly at the jump times of a Poisson process.