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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.07671 |
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| _version_ | 1866929588980940800 |
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| author | Yaran, Celal Umut Çağlar, Mine |
| author_facet | Yaran, Celal Umut Çağlar, Mine |
| contents | We study general Markov additive processes when the state space of the modulator is a Polish space. Under some regularity assumptions, our main result is the characterization of the long-time behavior of the ordinate in terms of the associated ladder time process and the excursion measure. An important application of Markov additive processes is the Lamperti-Kiu transform, which gives a correspondence between $\mathbb{R}^d\backslash \{0\}$-valued self-similar Markov processes and $S^{d-1}\times \mathbb{R}$-valued Markov additive processes. The asymptotic behavior of the radial distance from the origin of a self-similar Markov process can be characterized by the long-time behavior of the ordinate of the corresponding Markov additive process. We show the applicability of our assumptions on some well-known self-similar Markov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long Time Behavior of General Markov Additive Processes Yaran, Celal Umut Çağlar, Mine Probability 60G18, 60G51, 60J25 We study general Markov additive processes when the state space of the modulator is a Polish space. Under some regularity assumptions, our main result is the characterization of the long-time behavior of the ordinate in terms of the associated ladder time process and the excursion measure. An important application of Markov additive processes is the Lamperti-Kiu transform, which gives a correspondence between $\mathbb{R}^d\backslash \{0\}$-valued self-similar Markov processes and $S^{d-1}\times \mathbb{R}$-valued Markov additive processes. The asymptotic behavior of the radial distance from the origin of a self-similar Markov process can be characterized by the long-time behavior of the ordinate of the corresponding Markov additive process. We show the applicability of our assumptions on some well-known self-similar Markov processes. |
| title | Long Time Behavior of General Markov Additive Processes |
| topic | Probability 60G18, 60G51, 60J25 |
| url | https://arxiv.org/abs/2411.07671 |