Antonelli, FabioKohatsu, ArturoUniversitat Pompeu Fabra. Departament d'Economia i Empresa2017-07-262017-07-261998-08-01Annals of Applied Probability, 12, (2002), pp. 423-476http://hdl.handle.net/10230/693This 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.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPapermc kean-vlasov equationmalliavin calculusStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess