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

Sandro Gallo
Source: Adv. in Appl. Probab. Volume 43, Number 3 (2011), 735-759.

#### Abstract

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.

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Primary Subjects: 60G10
Secondary Subjects: 60G99
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1316792668
Digital Object Identifier: doi:10.1239/aap/1316792668
Zentralblatt MATH identifier: 05955084
Mathematical Reviews number (MathSciNet): MR2858219

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