Perfect Simulation and Convex Mixture of Context Trees

Abstract

Chains with unbounded memory have attracted lot of attention since the 30s and the pioneering work of Onicescu and Mihoc (Bull Sci Math 59(2):174–192, 1935) and Doeblin and Fortet (Bull Soc Math France 65:132–148, 1937). The construction of perfect simulation algorithm for these chains was first presented in the beginning of the century, and the particular case of discontinuous cases was first studied in the 2010s. The present paper presents a particular approach to perfect simulation of possibly discontinuous chains with unbounded memory. The main idea is to use a representation of the kernel through a convex mixture of probabilistic context trees.