Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space
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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
quasi-monte carlo method markov chain simulation discrepancy