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arXiv · 1801.06684

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

Dawid Czapla·Joanna Kubieniec
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Abstract

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 generalise a result of J. Kazak on the jump process defined by a Poisson driven stochastic differential equation with a solution-dependent intensity of perturbations.

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Dawid Czapla, Joanna Kubieniec. 2018-01-20. Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation. https://doi.org/10.1080/14689367.2018.1485879

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