|The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
|Year of Publication
|Czapla D, Horbacz K, Wojewódka-Ściążko H
|Qualitative Theory of Dynamical Systems
|Bounded-Lipschitz distance, central limit theorem, exponential ergodicity, Markov process, Martingale method
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.