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

TitleThe central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
Publication TypeJournal Article
Year of Publication2023
AuthorsCzapla D, Horbacz K, Wojewódka-Ściążko H
Journal Qualitative Theory of Dynamical Systems
Volume23
Issue7
Date Published09/2023
KeywordsBounded-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.

URLhttps://doi.org/10.1007/s12346-023-00862-4
DOI10.1007/s12346-023-00862-4

Historia zmian

Data aktualizacji: 20/10/2023 - 15:18; autor zmian: Hanna Wojewódka Ściążko (hws@iitis.pl)