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

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pierre L’Ecuyer & Christian Lécot & Bruno Tuffin, 2006. "Randomized Quasi-Monte Carlo Simulation of Markov Chains with an Ordered State Space," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 331-342, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_19
    DOI: 10.1007/3-540-31186-6_19
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