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Contributions à l'analyse numérique des méthodes quasi-Monte Carlo

Abstract : Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods. Random numbers are replaced by low discrepancy point sets. The error of a quasi-Monte Carlo method is estimated by means of the discrepancy of the sequence used. First, we are interested in solving ODE's with non-smooth coefficients by quasi-Monte Carlo methods. This is accomplished by treating the problem as being equivalent to the evaluation of an integral. Next, quasi-Monte Carlo particle methods are described for solving the following kinetic equations: linear Boltzmann equation and Kac equation. Finally, we propose a particle scheme using quasi-random walks for diffusion equations. These methods contain three steps: an Euler scheme, a particle approximation and a quasi-Monte Carlo quadrature using $(0,m,s)$-nets. The particles are relabeled at each time step. Then, convergence is proved. The numerical experiments show that better results are obtained with quasi-Monte Carlo methods than with Monte Carlo methods.
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Submitted on : Friday, February 20, 2004 - 3:17:08 PM
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  • HAL Id : tel-00004933, version 1



Ibrahim Coulibaly. Contributions à l'analyse numérique des méthodes quasi-Monte Carlo. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1997. Français. ⟨tel-00004933⟩



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