Quantitative Convergence Rates for Stochastically Monotone Markov Chains

2024/09/30 by Takashi Kamihigashi, John Stachurski, Kamihigashi, Takashi +1
Mathematics · #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2409.19874

Abstract

For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic mixing conditions. We complement these results by providing quantitative bounds on deviations between distributions. We also show that well-known total variation bounds can be recovered as a special case.

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