Rate of convergence of a particle method to the solution of the McKean-Vlasov equation
type: Item
instance of: scholarly article
title: Rate of convergence of a particle method to the solution of the McKean-Vlasov equation
zbMATH Open document ID: 1015.60048
author: Fabio Antonelli
author: Arturo Kohatsu-Higa
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the McKean-Vlasov equation introduced by Bossy and Talay. More specifically, the authors consider approximations of the distribution and of the density of the solution of the stochastic differential equation associated to the McKean-Vlasov equation. The scheme adopted here is a mixed one: Euler-weakly interacting particle system. If \(n\) is the number of weakly interacting particles and \(h\) is the uniform step in the time discretization, they prove that the rate of convergence of the distribution functions of the approximating sequence in the \(L^1(\Omega\times R)\) norm is of the order of \(1/(\sqrt{n}+h)\), while for the densities is of the order \((h+1)/\sqrt{n}h^{1/4}\). The rates of convergence with respect to the supremum norm are also calculated. This result is obtained by carefully employing techniques of Malliavin calculus.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 1906170
zbMATH Keywords: McKean-Vlasov equation
zbMATH Keywords: Malliavin calculus
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1026915611
OpenAlex ID: W2086872802
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DOI: 10.1214/AOAP/1026915611
description: scientific article; zbMATH DE number 1906170