English

Compressibility and Stochastic Stability of Monotone Markov Chain

Probability 2026-04-02 v2

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.

Keywords

Cite

@article{arxiv.2403.15259,
  title  = {Compressibility and Stochastic Stability of Monotone Markov Chain},
  author = {Sergey Foss and Michael Scheutzow},
  journal= {arXiv preprint arXiv:2403.15259},
  year   = {2026}
}

Comments

23 pages