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Monte Carlo (MC) method is probably the most widespread simulation technique due to its ease of use. Quasi-Monte Carlo (QMC) methods have been designed in order to speed up the convergence rate of MC but their implementation requires more stringent assumptions. For instance, the direct QMC simulation of Markov chains is inefficient due to the correlation of the points used. We propose here to survey the QMC-based methods that have been developed to tackle the QMC simulation of Markov chains. Most of those methods were hybrid MC/QMC methods. We compare them with a recently developped pure QMC method and illustrate the better convergence speed of the latter.

Comparison of Quasi-Monte Carlo-Based Methods for Simulation of Markov Chains