A general context-tree-based approach to perfect simulation for chains of infinite order

Details A general context-tree-based approach to perfect simulation for chains of infinite order A general context-tree-based approach to perfect simulation for chains of infinite order

2011-03-10

arxiv.org/abs/1103.2058v3

Mathematics

Probability

37 pages, 15 figures, new results have been added, some corrections have been done

Scientific paper

We establish new sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. This is done through the introduction of the \emph{localized continuity} assumption. This new assumption, which is formalized with the help of the notion of \emph{context trees}, includes the traditional continuous case, probabilistic context trees and discontinuous kernels. Since our assumptions are more refined than uniform continuity, our algorithms perfectly simulate continuous chains faster than the existing algorithms of the literature. We also give a simple extension of the method allowing to perfectly simulate chains which are neither necessarily continuous nor necessarily weakly non-null.

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