Diffusion processes associated with nonlinear evolution equations for signed measures
type: Item
instance of: scholarly article
title: Diffusion processes associated with nonlinear evolution equations for signed measures
zbMATH Open document ID: 0960.60092
DOI: 10.1023/A:1010059302049
published in: Methodology and Computing in Applied Probability
publication date: 2001-05-13T00:00:00Z
review text: The author is interested in probabilistic particle approximations of the solution of a nonlinear parabolic evolution equation starting at a bounded signed measure. His approach generalizes results obtained when the initial condition is a probability measure. One introduces a nonlinear martingale problem, under the solution \(P\) of which one recovers the solution of the partial differential equation. Here, the originality consists in giving to each sample path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation, the author is interested in a viscous scalar conservation law. He proves uniqueness for the associated nonlinear martingale problem and obtains existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Then he studies the associated fluctuations and presents numerical results which confirm the theoretical rate of convergence.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1501446
zbMATH Keywords: nonlinear martingale problem
zbMATH Keywords: propagation of chaos
zbMATH Keywords: fluctuations
author: Benjamin Jourdain
reviewed by: Sylvie Méléard
MaRDI profile type: Publication
full work available at URL: a:1010059302049
OpenAlex ID: W1555593000
description: scientific article; zbMATH DE number 1501446