A strong law of large numbers for strongly mixing processes

A. Kontorovich, A. Brockwell

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)3777-3796
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Issue number18
StatePublished - 1 Jan 2014


  • Concentration
  • Lawof large numbers
  • Markov Chain Monte Carlo
  • Mixing

ASJC Scopus subject areas

  • Statistics and Probability


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