Quantitative Convergence Rates for Stochastically Monotone Markov Chains

Takashi Kamihigashi; John Stachurski

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arXiv · 2409.19874

Quantitative Convergence Rates for Stochastically Monotone Markov Chains

Takashi Kamihigashi·John Stachurski

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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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Takashi Kamihigashi, John Stachurski. 2024-09-30. Quantitative Convergence Rates for Stochastically Monotone Markov Chains. https://arxiv.org/abs/2409.19874

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