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