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arXiv · 2404.11432

Quantitative merging for time-inhomogeneous Markov chains in non-decreasing environments via functional inequalities

Nordine Moumeni
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Abstract

We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincar\'e, 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.

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Nordine Moumeni. 2024-04-17. Quantitative merging for time-inhomogeneous Markov chains in non-decreasing environments via functional inequalities. https://arxiv.org/abs/2404.11432

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