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arXiv · 2403.15259

Compressibility and Stochastic Stability of Monotone Markov Chain

Sergey Foss·Michael Scheutzow
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Abstract

For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular, we generalise a basic result by Bhattacharya and Majumdar (2007) where a certain form of mixing, or swap condition was assumed uniformly over the state space. We do not rely on continuity properties of transition probabilities.

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Sergey Foss, Michael Scheutzow. 2024-03-22. Compressibility and Stochastic Stability of Monotone Markov Chain. https://arxiv.org/abs/2403.15259

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