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.
BT - Qualitative Theory of Dynamical Systems DA - 09/2023 DO - 10.1007/s12346-023-00862-4 IS - 7 LA - eng N2 -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.
PY - 2024 T2 - Qualitative Theory of Dynamical Systems TI - The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm UR - https://doi.org/10.1007/s12346-023-00862-4 VL - 23 ER -