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September 2011 Chains with unbounded variable length memory: perfect simulation and a visible regeneration scheme
Sandro Gallo
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Adv. in Appl. Probab. 43(3): 735-759 (September 2011). DOI: 10.1239/aap/1316792668

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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Sandro Gallo. "Chains with unbounded variable length memory: perfect simulation and a visible regeneration scheme." Adv. in Appl. Probab. 43 (3) 735 - 759, September 2011. https://doi.org/10.1239/aap/1316792668

Information

Published: September 2011
First available in Project Euclid: 23 September 2011

zbMATH: 1229.60041
MathSciNet: MR2858219
Digital Object Identifier: 10.1239/aap/1316792668

Subjects:
Primary: 60G10
Secondary: 60G99

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 3 • September 2011
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