Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation

摘要

We are concerned with the asymptotics of the Markov chain given by the post-jump locations of a certain piecewise-deterministic Markov process with a state-dependent jump intensity. We provide sufficient conditions for such a model to possess a unique invariant distribution, which is exponentially attracting in the dual-bounded Lipschitz distance. Having established this, we generalize a result of J. Kazak on the jump process defined by a Poisson-driven stochastic differential equation with a solution-dependent intensity of perturbations.