# 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.
Keywords :
Document type :
Theses
Domain :

Cited literature [62 references]

https://tel.archives-ouvertes.fr/tel-00004933
Contributor : Thèses Imag <>
Submitted on : Friday, February 20, 2004 - 3:17:08 PM
Last modification on : Wednesday, March 10, 2021 - 1:50:03 PM
Long-term archiving on: : Thursday, September 13, 2012 - 2:05:44 PM

### Identifiers

• HAL Id : tel-00004933, version 1

### Citation

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

Record views