A. Yu. Golubin, “A new condition for ergodicity of Markov chains with a general state space”, Teor. Veroyatnost. i Primenen., 2025, Volume 70, Issue 1,Pages <nobr>182

Short Communications

A new condition for ergodicity of Markov chains with a general state space

A. Yu. Golubin^ab

^a National Research University Higher School of Economics, Moscow
^b Center of Information Technologies in Design, Russian Academy of Sciences, Odintsovo, Moscow region

Abstract: The paper suggests a new condition, specifically a two-set decomposition of a Markov chain, guaranteeing the existence of a unique stationary distribution of the Markov chain with a general state space. This condition turns out to be sufficient for ergodicity of the Markov chain under the Harris recurrent condition. A comparison of the suggested condition with the known Doeblin condition and $\phi$-irreduciblity condition is given, and a concrete illustrative example is provided.

Keywords: Markov chain, stationary distribution, ergodicity.

Received: 11.01.2024
Revised: 09.10.2024

DOI: 10.4213/tvp5700