dc.contributor.author Antonelli, Fabio dc.contributor.author Kohatsu-Higa, Arturo dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa dc.date.accessioned 2012-07-11T02:07:35Z dc.date.available 2012-07-11T02:07:35Z dc.date.issued 2005-09-15T23:09:54Z 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.rights.uri Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el departament i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) dc.subject.other Mc Kean-Vlasov equation, Malliavin calculus 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 2012-07-10T07:27:31Z

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