Comparison Theorems for Reversible Markov Chains

Comparison Theorems for Reversible Markov Chains

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Renewal Theorems for Markov Chains

weak-reversible Markov chains

The theory of L-spectral gaps for reversible Markov chains has been studied by many authors. In this paper we consider positive recurrent general state space Markov chains with stationary transition probabilities. Replacing the assumption of reversibility by a less strong one, we still obtain a simple necessary and sufficient condition for the spectral gap property of the associated Markov oper...

Ratio Limit Theorems for Markov Chains

Introduction. We consider Markov chains with stationary transition probabilities and state space S = 0, 1, 2, •• -, in both discrete and continuous time. As in [l ] the transition probabilities are denoted by pi}1 (indiscrete time) and pa(t) (in continuous time). We assume that the chains considered are irreducible and recurrent, and in addition that discrete time chains are aperiodic and that ...

Limit Theorems for subgeometric Markov chains

This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the Foster-Lyapunov conditions. The regeneration-split chain method...