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 Title: Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation Antonelli, Fabio; Kohatsu, Arturo Universitat Pompeu Fabra. Departament d'Economia i Empresa This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h$, while for the densities is ofthe order $h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus. 2005-09-15 Statistics, Econometrics and Quantitative Methodsmc kean-vlasov equationmalliavin calculus L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Working Paper

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