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

TytułThe central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
Publication TypeJournal Article
Rok publikacji2022
AutorzyCzapla D, Horbacz K, Wojewódka-Ściążko H
Journalarxiv.2210.11963, submitted
Słowa kluczowe37A30, 46E27, 60J25, FOS: Mathematics, Probability (math.PR)
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 \hbox{example}, we verify the assumptions of our main result for a specific piecewise-deterministic Markov process, whose continuous component evolves according to semiflows, switched randomly at the jump times of a~Poisson process.

URLhttps://arxiv.org/abs/2210.11963
DOI10.48550/ARXIV.2210.11963