Showing papers by "Benjamin Jourdain published in 1998"
TL;DR: In this article, a stochastic differential equation which is nonlinear in the sense that both the diffusion and the drift coefficients depend locally on the density of the time marginal of the solution was studied.
Abstract: In this paper, we are interested in a stochastic differential equation which is nonlinear in the following sense: both the diffusion and the drift coefficients depend locally on the density of the time marginal of the solution. When the law of the initial data has a smooth density with respect to Lebesgue measure, we prove existence and uniqueness for this equation. Under more restrictive assumptions on the density, we approximate the solution by a system of n moderately interacting diffusion processes and obtain a trajectorial propagation of chaos result. Finally, we study the fluctuations associated with the convergence of the empirical measure of the system to the law of the solution of the nonlinear equation. In this situation, the convergence rate is different from √ n .
106 citations
TL;DR: In this article, the authors give a probabilistic interpretation of the solution of a diffusion-convection equation and obtain the solution as the propagation of chaos limit of a sequence of moderately interacting particle systems.
3 citations