Perfect simulation for locally continuous chains of infinite order

TL;DR

This paper introduces a new localized continuity condition for perfect simulation of infinite order chains, enabling faster algorithms and broader applicability than previous methods.

Contribution

It formalizes localized continuity using context trees, extending perfect simulation techniques to include discontinuous kernels and probabilistic context trees.

Findings

Faster perfect simulation algorithms for continuous chains.

Broader applicability to discontinuous kernels.

Includes illustrative examples demonstrating effectiveness.

Abstract

We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and 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 provide several illustrative examples.