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Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Rami El Haddad

    (Université Saint-Joseph, Département de Mathématiques)

  • Christian Lécot

    (Université de Savoie, LAMA)

  • Pierre L’Ecuyer

    (Université de Montréal, DIRO)

Abstract

Summary We propose and analyze a quasi-Monte Carlo (QMC) method for simulating a discrete-time Markov chain on a discrete state space of dimension s ≥ 1. Several paths of the chain are simulated in parallel and reordered at each step, using a multidimensional matching between the QMC points and the copies of the chains. This method generalizes a technique proposed previously for the case where s = 1. We provide a convergence result when the number N of simulated paths increases toward infinity. Finally, we present the results of some numerical experiments showing that our QMC algorithm converges faster as a function of N, at least in some situations, than the corresponding Monte Carlo (MC) method.

Suggested Citation

  • Rami El Haddad & Christian Lécot & Pierre L’Ecuyer, 2008. "Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 413-429, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_24
    DOI: 10.1007/978-3-540-74496-2_24
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