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

Autorzy Czapla D.; Horbacz K.; Wojewódka-Ściążko H.
Tytuł The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
Czasopismo Qualitative Theory of Dynamical Systems
Rok 2024
Status Published
Tom 23
Numer 7
DOI 10.1007/s12346-023-00862-4
URL https://doi.org/10.1007/s12346-023-00862-4
Abstrakt <p>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&nbsp;Poisson process.</p>