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1 results

  • Return times in nearly-completely decomposable stochastic processes

  • G. Latouche, G. Louchard
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 251-267
    Print publication:
    June 1978

  • Consider a finite irreducible aperiodic Markov chain with nearly-completely decomposable stochastic matrix: i.e. a Markov chain for which the states can be grouped into disjoint aggregates, in such a way that the probabilities of transition between states of the same aggregate are large compared to the probabilities of transition between states belonging to different aggregates. Let Ω be a subset of one of the aggregates. Second-order approximations are determined for the first and second moments of the time to reach Ω and the return time to Ω.