Chains with unbounded variable length memory: perfect simulation and visible regeneration scheme
Abstract
We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite 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
Cite
@article{arxiv.0907.2150,
title = {Chains with unbounded variable length memory: perfect simulation and visible regeneration scheme},
author = {Sandro Gallo},
journal= {arXiv preprint arXiv:0907.2150},
year = {2010}
}
Comments
27 pages, 10 figures, slight improvements of the results and simplification of the proof, simulations.