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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1907.05605 |
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| _version_ | 1866915557964513280 |
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| author | Grimmett, Geoffrey R. Holmes, Mark |
| author_facet | Grimmett, Geoffrey R. Holmes, Mark |
| contents | The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all trajectories. The issue of the coalescence or non-coalescence of trajectories of a finite state space Markov chain is investigated in this note. The notion of the 'coalescence number' $k(μ)$ of a Markovian coupling $μ$ is introduced, and results are presented concerning the set $K(P)$ of coalescence numbers of couplings corresponding to a given transition matrix $P$. Note: This is a revision of the original published version, in which part of Theorem 6 has been removed. A correction may be found in Thm 5.3 of arXiv:2510.13572. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_05605 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Non-coupling from the past Grimmett, Geoffrey R. Holmes, Mark Probability 60J10, 60J22 The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all trajectories. The issue of the coalescence or non-coalescence of trajectories of a finite state space Markov chain is investigated in this note. The notion of the 'coalescence number' $k(μ)$ of a Markovian coupling $μ$ is introduced, and results are presented concerning the set $K(P)$ of coalescence numbers of couplings corresponding to a given transition matrix $P$. Note: This is a revision of the original published version, in which part of Theorem 6 has been removed. A correction may be found in Thm 5.3 of arXiv:2510.13572. |
| title | Non-coupling from the past |
| topic | Probability 60J10, 60J22 |
| url | https://arxiv.org/abs/1907.05605 |