The Central Limit Theorem for Markov Processes that are Exponentially Ergodic in the Bounded-Lipschitz Norm

• Dawid Czapla ^[1] ; Katarzyna Horbacz ^[1] ; Hanna Wojewódka-Sciazko ^[1]
  1. [1] University of Silesia

     University of Silesia

     Katowice, Polonia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • 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.