Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques

Abstract : This thesis is divided into two independent parts. In the first one, we are interested in a microscopic individual-based model for the description of a population structured by traits and ages. We study the ecology of the system (population dynamics problems) in a large population asymptotics. Under appropriate renormalizations, the microscopic process converges to the measure solution of a deterministic evolution equation. A Central Limit Theorem and the exponential deviations of this convergence are studied. These results are used to generalize some evolution models from the recent theory of adaptive dynamics to age-structured populations. These models describe the evolution of the trait structure of a population on large time scales and under the assumptions of rare (and possibly small) mutations and large populations. In the second part of this thesis, we consider McKean-Vlasov and 2D Navier-Stokes partial differential equations with random initial conditions. The law of the solutions, which are then random variables, is called statistical solution. Using a probabilistic approach for these equations, we propose original stochastic wavelet particle approximations for the moments of order 1 of the statistical solutions, and study the convergence rates of the proposed procedures.
Document type :
Theses
Mathematics [math]. Université de Nanterre - Paris X, 2006. French


https://tel.archives-ouvertes.fr/tel-00125100
Contributor : Viet Chi Tran <>
Submitted on : Wednesday, January 17, 2007 - 9:13:06 PM
Last modification on : Thursday, January 18, 2007 - 12:36:36 PM

Identifiers

  • HAL Id : tel-00125100, version 1

Collections

Citation

Viet Chi Tran. Modèles particulaires stochastiques pour des problèmes d'évolution adaptative et pour l'approximation de solutions statistiques. Mathematics [math]. Université de Nanterre - Paris X, 2006. French. <tel-00125100>

Export

Share

Metrics

Consultation de
la notice

517

Téléchargement du document

313