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Chains with unbounded variable length memory: perfect simulation and a visible regeneration scheme

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Sandro Gallo
Sandro Gallo*
Affiliation:
University of Campinas
*
∗ Postal address: University of Campinas, Rua Sérgio Buarque de Holanda 651, CEP 13083-859 Campinas, São Paulo, Brazil. Email address: gsandro@ime.unicamp.br
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Abstract

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We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infinite memory chains for which the family of transition probabilities is represented by a probabilistic context tree. We do not assume any continuity condition: our condition is expressed in terms of the structure of the context tree. More precisely, the length of the contexts is a deterministic function of the distance to the last occurrence of some determined string of symbols. It turns out that the resulting class of chains can be seen as a natural extension of the class of chains having a renewal string. In particular, our chains exhibit a visible regeneration scheme.

Keywords

Variable length memory chainprobabilistic context treeperfect simulationregeneration scheme

MSC classification

Primary: 60G10: Stationary processes
Secondary: 60G99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 3 , September 2011 , pp. 735 - 759
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

This work forms part of the USP Project ‘Mathematics, Computation, Language and the Brain’. Research supported by an FAPESP fellowship (grant number 2006/57387-0).

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