Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures |
| |
Authors: | B. Jourdain |
| |
Affiliation: | (1) ENPC-CERMICS, 6-8 av Blaise Pascal, Cite´ Descartes, Champs sur Marne, 77455 Marne la Valle´e Cedex 2, France |
| |
Abstract: | In this paper, we explain how to associate a nonlinear martingale problem with some nonlinear parabolic evolution equations starting at bounded signed measures. Our approach generalizes the classical link made when the initial condition is a probability measure. It consists in giving to each sample-path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation as an introductory example, we are interested in a viscous scalar conservation law. We prove uniqueness for the corresponding nonlinear martingale problem and then obtain existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Last, we study the behavior of the associated fluctuations and present numerical results which confirm the theoretical rate of convergence. |
| |
Keywords: | nonlinear martingale problem propagation of chaos fluctuations |
本文献已被 SpringerLink 等数据库收录! |
|