Randomized Quasi-Monte Carlo Simulation of Markov Chains with an Ordered State Space

Pierre L’Ecuyer (), Christian Lécot () and Bruno Tuffin ()
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Pierre L’Ecuyer: Université de Montréal, Département d’informatique et de recherche opérationnelle
Christian Lécot: Université de Savoie, Laboratoire de Mathématiques
Bruno Tuffin: Campus Universitaire de Beaulieu, IRISA-INRIA

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 331-342 from Springer

Abstract: Summary We study a randomized quasi-Monte Carlo method for estimating the state distribution at each step of a Markov chain with totally ordered (discrete or continuous) state space. The number of steps in the chain can be random and unbounded. The method simulates n copies of the chain in parallel, using a (d+1)-dimensional low-discrepancy point set of cardinality n, randomized independently at each step, where d is the number of uniform random numbers required at each transition of the Markov chain. The method can be used in particular to get a lowvariance unbiased estimator of the expected total cost up to some random stopping time, when state-dependent costs are paid at each step. We provide numerical illustrations where the variance reduction with respect to standard Monte Carlo is substantial.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_19

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DOI: 10.1007/3-540-31186-6_19

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