A Strong Law of Large Numbers for Strongly Mixing Processes

2008/07/29 by Aryeh Kontorovich, Kontorovich, Aryeh, Anthony Brockwell +1
Economics, Econometrics and Finance · Mathematics · #60F15 #60G35 #60J10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:60F15 #msc:60G35 #msc:60J10 #stat.TH

paper · pdf · doi:10.48550/arxiv.0807.4665

24 pages

arxiv created 2008/07/29 · openalex publication_date 2008/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic) bounds, with readily computable rate constants. In particular, this makes it suitable for analysis of inhomogeneous Markov processes. We demonstrate how it can be applied to establish an almost-sure convergence result for a class of models that includes as a special case a class of adaptive Markov chain Monte Carlo algorithms.

Citations

• A tutorial on hidden Markov models and selected applications in speech recognition

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