A Strong Law of Large Numbers for Strongly Mixing Processes

A. Kontorovich and A. Brockwell

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 18, 3777-3796

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.

Date: 2014
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DOI: 10.1080/03610926.2012.701696

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