On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes With State-Dependent Jump Intensity
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909210577469440 |
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| author | Czapla, Dawid |
| author_facet | Czapla, Dawid |
| contents | In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11576 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes With State-Dependent Jump Intensity Czapla, Dawid Probability Primary: 60J25, 60J05, Secondary: 60J35, 37A30 In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations. |
| title | On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes With State-Dependent Jump Intensity |
| topic | Probability Primary: 60J25, 60J05, Secondary: 60J35, 37A30 |
| url | https://arxiv.org/abs/2303.11576 |