Para-Markov chains and related non-local equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929641341583360 |
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| author | Facciaroni, Lorenzo Ricciuti, Costantino Scalas, Enrico Toaldo, Bruno |
| author_facet | Facciaroni, Lorenzo Ricciuti, Costantino Scalas, Enrico Toaldo, Bruno |
| contents | There is a well established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times, although marginally Mittag-Leffler, are assumed to be stochastically dependent. This creates a long memory tail in the evolution, unlike what happens for semi-Markov processes. As a special case of our chains, we study a particular counting process which extends the well-known fractional Poisson process, the last one having independent, Mittag-Leffler waiting times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Para-Markov chains and related non-local equations Facciaroni, Lorenzo Ricciuti, Costantino Scalas, Enrico Toaldo, Bruno Probability 60G99 There is a well established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times, although marginally Mittag-Leffler, are assumed to be stochastically dependent. This creates a long memory tail in the evolution, unlike what happens for semi-Markov processes. As a special case of our chains, we study a particular counting process which extends the well-known fractional Poisson process, the last one having independent, Mittag-Leffler waiting times. |
| title | Para-Markov chains and related non-local equations |
| topic | Probability 60G99 |
| url | https://arxiv.org/abs/2412.14979 |