%0 Journal Article %1 czapla2018exponential %A Czapla, Dawid %A Kubieniec, Joanna %D 2018 %K PDMP %T Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation %U http://arxiv.org/abs/1801.06684 %X 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.

@article{czapla2018exponential, 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.}, added-at = {2018-01-23T14:42:22.000+0100}, author = {Czapla, Dawid and Kubieniec, Joanna}, biburl = {https://www.bibsonomy.org/bibtex/2b43ca967fa376e59d02c97fb74721033/claired}, description = {Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation}, interhash = {da58908e2447af404e179a1faef5bf2a}, intrahash = {b43ca967fa376e59d02c97fb74721033}, keywords = {PDMP}, note = {cite arxiv:1801.06684}, timestamp = {2018-01-23T14:42:22.000+0100}, title = {Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation}, url = {http://arxiv.org/abs/1801.06684}, year = 2018 }