Compressibility and stochastic stability of monotone Markov chains
- 1 October 2026
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 36 (5) , 4516-4534
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 (Random Dynamical Systems: Theory and Applications (2007) Cambridge Univ. Press) where a certain form of mixing, or splitting condition was assumed uniformly over the state space. We do not rely on continuity properties of transition probabilities.Keywords
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