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Solidarity properties and a Doeblin decomposition for a class of non-Markovian stochastic processes

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Abstract

We are concerned with solidarity and a Doeblin decomposition for a class of non-Markovian discrete parameter stochastic processes. Since any such process is associated with a certain general Markov chain whose transition probability function has a special form, we use the theory of Markov chains with continuous components to this particular chain in order to get properties of the non-Markovian process. We illustrate our results on a model closely related to learning theory.

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Authors and Affiliations

  1. Département de mathematiques, Université Laval, G1K 7P4, Québec, PQ, Canada

    R. Theodorescu

  2. Division of Mathematics and Statistics, C.S.I.R.O., P.O. Box 310, 3205, South Melbourne, Victoria, Australia

    R. L. Tweedie

Authors
  1. R. Theodorescu
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  2. R. L. Tweedie
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Additional information

Work supported by the Natural Sciences and Engineering Council Canada grant A-7223, by the Québec Action Concertée grant EQ-1023, and the C.S.I.R.O. Division of Mathematics and Statistics Australia.

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Theodorescu, R., Tweedie, R.L. Solidarity properties and a Doeblin decomposition for a class of non-Markovian stochastic processes. Metrika 30, 37–47 (1983). https://doi.org/10.1007/BF02056899

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  • DOI: https://doi.org/10.1007/BF02056899

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