The Borel-Cantelli Lemma for Markov Sequences of Events

TL;DR

This paper introduces a new generalization of the Borel-Cantelli lemma tailored for Markov sequences, enabling stronger limit results for Markov chains with practical applications.

Contribution

It presents a novel generalization of the Borel-Cantelli lemma specifically for Markov sequences, expanding its applicability to Markov chain analysis.

Findings

Derived strong limit results for Markov chains.

Provided illustrative applications demonstrating the generalization.

Enhanced understanding of event occurrence probabilities in Markov processes.

Abstract

In the present paper, we propose a new generalization of the Borel-Cantelli lemma. This generalization can be further used to derive strong limit results for Markov chains. Illustrative applications are provided.