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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22836 |
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| _version_ | 1866909976986910720 |
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| author | Golomoziy, Vitaliy |
| author_facet | Golomoziy, Vitaliy |
| contents | In this paper, we consider a modified version of a well-known submartingale condition fortheweak convergence of probabilitymeasures, adapted to the semi-Markov case. In this setting, it is convenient to work with an embedded Markov chain and the filtration generated by jump times. We demonstrate that a straightforward restatement of the classical result is not valid, and that an additional condition is required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Submartingale Condition for Weak Convergence for Semi-Markov Processes Golomoziy, Vitaliy Probability 60B10, 60K15 In this paper, we consider a modified version of a well-known submartingale condition fortheweak convergence of probabilitymeasures, adapted to the semi-Markov case. In this setting, it is convenient to work with an embedded Markov chain and the filtration generated by jump times. We demonstrate that a straightforward restatement of the classical result is not valid, and that an additional condition is required. |
| title | Submartingale Condition for Weak Convergence for Semi-Markov Processes |
| topic | Probability 60B10, 60K15 |
| url | https://arxiv.org/abs/2512.22836 |