# Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

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Annals of Applied Probability, 12, (2002), pp. 423-476
http://hdl.handle.net/10230/693
 To cite or link this document: http://hdl.handle.net/10230/693
 dc.contributor.author Antonelli, Fabio dc.contributor.author Kohatsu, Arturo dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa dc.date.issued 1998-08-01 dc.identifier.citation Annals of Applied Probability, 12, (2002), pp. 423-476 dc.identifier.uri http://hdl.handle.net/10230/693 dc.description.abstract This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the Mc Kean-Vlasov equation introduced by Bossy and Talay. More specifically, we consider approximations of the distribution and of the density of the solution of the stochastic differential equation associated to the Mc Kean - 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, we prove that the rate of convergence of the distribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of the order of $\frac 1{\sqrt n} + h$, while for the densities is of the order $h +\frac 1 {\sqrt {nh}}$. This result is obtained by carefully employing techniques of Malliavin Calculus. dc.language.iso eng dc.relation.ispartofseries Economics and Business Working Papers Series; 311 dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.title Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation dc.type info:eu-repo/semantics/workingPaper dc.date.modified 2014-06-03T07:13:56Z dc.subject.keyword Statistics, Econometrics and Quantitative Methods dc.subject.keyword mc kean-vlasov equation dc.subject.keyword malliavin calculus dc.rights.accessRights info:eu-repo/semantics/openAccess
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