# Coupling, renewal and perfect
simulation of chains of infinite order (ps)

### R. Fernandez, P. A. Ferrari, A. Galves

#### Notes for a Course in the V Brazilian School of Probability, Ubatuba
2001.

This is a 95 pages booklet developing an explicit construction of chains with
infinite memory under the Harris regime. Some of the topics in the summary are

Transition probabilities

Simulation algorithms and transition probabilities

Coupling and coupling algorithms

Types of chains of infinite order

Countable mixtures of Markov chains (CMMC)

Variable-length Markov chains (VLMC)

Sparse VLMC

Hidden Markov models (HMM)

Binary autoregressions

Random systems with complete connections

A regeneration scheme for CMMC

Existence, uniqueness and loss of memory of CMMC

Mixing properties and perfect simulations for CMMC

Every chain of infinite order is a CMMC and a VLMC

Markov approximations for chains of infinite order

Pablo A. Ferrari Home Page;
PAF's list of publications

Last modified: Fri Feb 1 16:40:43 EDT 2002