The Key Renewal Theorem for a Transient Markov Chain

2007/11/14 by Dmitry Korshunov, Korshunov, Dmitry
Mathematics · #60K05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60K05

paper · pdf · doi:10.48550/arxiv.0711.2169

12 pages

arxiv created 2007/11/14 · openalex publication_date 2007/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a time-homogeneous Markov chain X_n, n≥0, valued in \bf R. Suppose that this chain is transient, that is, X_n generates a σ-finite renewal measure. We prove the key renewal theorem under condition that this chain has asymptotically homogeneous at infinity jumps and asymptotically positive drift.

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