Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space

Authors:
R. El Haddad;C. Lécot;P. L'Ecuyer;N. Nassif
Affiliations:
Département de Mathématiques, Université Saint-Joseph, BP 11-514, Riad El Solh Beyrouth 1107 2050, Lebanon;LAMA, UMR 5127 CNRS & Universitéé de Savoie, 73376 Le Bourget du Lac, France;Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, CP 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada;Department of Mathematics, American University of Beirut, BP 11-0236, Riad El-Solh Beyrouth 1107 2020, Lebanon
Venue:
Mathematics and Computers in Simulation
Year:
2010

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Abstract

We describe a quasi-Monte Carlo method for the simulation of discrete time Markov chains with continuous multi-dimensional state space. The method simulates copies of the chain in parallel. At each step the copies are reordered according to their successive coordinates. We prove the convergence of the method when the number of copies increases. We illustrate the method with numerical examples where the simulation accuracy is improved by large factors compared with Monte Carlo simulation.