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

2024/04/17 by Moumeni, Nordine
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2404.11432

Abstract

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.

Related

• Merging and stability for time inhomogeneous finite Markov chains
• Asymptotic Analysis of Multiscale Markov Chain
• Uniform Chernoff and Dvoretzky-Kiefer-Wolfowitz-type inequalities for Markov chains and related processes
• Bounds on Mixing Time for Time-Inhomogeneous Markov Chains
• Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis