Local limit theorems for inhomogeneous Markov chains

2021/09/12 by Dolgopyat, Dmitry, Sarig, Omri
Mathematics · #60F05 #60J05 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2109.05560

openalex publication_date 2021/09/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the large deviation regime for bounded additive functionals of uniformly elliptic Markov chains. The proofs rely on new reduction theorems for Markov arrays.

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