Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866916172453117952 |
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| author | Czapla, Dawid Kubieniec, Joanna |
| author_facet | Czapla, Dawid Kubieniec, Joanna |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1801_06684 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation Czapla, Dawid Kubieniec, Joanna Probability 37A30, 60J05, 60H10, 37H10 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. |
| title | Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equation |
| topic | Probability 37A30, 60J05, 60H10, 37H10 |
| url | https://arxiv.org/abs/1801.06684 |