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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.11432 |
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| _version_ | 1866909229868122112 |
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| author | Moumeni, Nordine |
| author_facet | Moumeni, Nordine |
| contents | We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincaré, Nash, and logarithmic-Sobolev inequalities. We assume that our Markov chain admits a finite invariant measure at each time and that the sequence of these invariant measures is non-decreasing. We deduce quantitative bounds on the merging time of the distributions for the chain started at two arbitrary points and we illustrate these new results with examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative merging for time-inhomogeneous Markov chains in non-decreasing environments via functional inequalities Moumeni, Nordine Probability We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincaré, Nash, and logarithmic-Sobolev inequalities. We assume that our Markov chain admits a finite invariant measure at each time and that the sequence of these invariant measures is non-decreasing. We deduce quantitative bounds on the merging time of the distributions for the chain started at two arbitrary points and we illustrate these new results with examples. |
| title | Quantitative merging for time-inhomogeneous Markov chains in non-decreasing environments via functional inequalities |
| topic | Probability |
| url | https://arxiv.org/abs/2404.11432 |