Tytuł | The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm |
Publication Type | Journal Article |
Rok publikacji | 2023 |
Autorzy | Czapla D, Horbacz K, Wojewódka-Ściążko H |
Journal | Qualitative Theory of Dynamical Systems |
Volume | 23 |
Issue | 7 |
Date Published | 09/2023 |
Słowa kluczowe | Bounded-Lipschitz distance, central limit theorem, exponential ergodicity, Markov process, Martingale method |
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. |
URL | https://doi.org/10.1007/s12346-023-00862-4 |
DOI | 10.1007/s12346-023-00862-4 |