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Imbedded construction of stationary sequences and point processes with a random memory

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Abstract

We show convergence in variation to a unique stationary state for a class of point processes (respectively, stochastic sequences) with stochastic intensity kernels (respectively, transition probabilities) including the (A,m)-processes of Lindvall [12]. This is done under two basic conditions: first, the random memory of the processes considered is consistent or non-reusable (that is, past information not used at a given time cannot be recalled at a later time) and secondly, the kernels have a deterministic fixed component for which the memory is almost surely finite.

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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau de Moulon, 91192, Gif-sur-Yvette, France

    Pierre Brémaud & Laurent Massoulié

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  1. Pierre Brémaud
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  2. Laurent Massoulié
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Brémaud, P., Massoulié, L. Imbedded construction of stationary sequences and point processes with a random memory. Queueing Syst 17, 213–234 (1994). https://doi.org/10.1007/BF01158695

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  • DOI: https://doi.org/10.1007/BF01158695

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