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.
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El Haddad, R., Lécot, C., L’Ecuyer, P. (2008). Quasi-Monte Carlo Simulation of Discrete-Time Markov Chains on Multidimensional State Spaces. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_24
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DOI: https://doi.org/10.1007/978-3-540-74496-2_24
Publisher Name: Springer, Berlin, Heidelberg
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