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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.17647 |
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| _version_ | 1866912299954995200 |
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| author | Pollett, Phil |
| author_facet | Pollett, Phil |
| contents | In a recent paper, Shah [arXiv:2502.03073] derived an explicit expression for the distribution of occupancy times for a two-state Markov chain, using a method based on enumerating sample paths. We consider here the more general problem of finding the distribution of occupancy times for countable-state Markov chains in discrete time. Our approach, which employs generating functions, leads to arguably simpler formulae for the occupancy distribution for the two-state chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the state occupancy distribution for Markov chains Pollett, Phil Probability In a recent paper, Shah [arXiv:2502.03073] derived an explicit expression for the distribution of occupancy times for a two-state Markov chain, using a method based on enumerating sample paths. We consider here the more general problem of finding the distribution of occupancy times for countable-state Markov chains in discrete time. Our approach, which employs generating functions, leads to arguably simpler formulae for the occupancy distribution for the two-state chain. |
| title | A note on the state occupancy distribution for Markov chains |
| topic | Probability |
| url | https://arxiv.org/abs/2503.17647 |