Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation
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- dc.contributor.author Antonelli, Fabioca
- dc.contributor.author Kohatsu, Arturoca
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2017-07-26T10:50:33Z
- dc.date.available 2017-07-26T10:50:33Z
- dc.date.issued 1998-08-01
- dc.date.modified 2017-07-23T02:03:50Z
- 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.format.mimetype application/pdfca
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=311
- dc.identifier.citation Annals of Applied Probability, 12, (2002), pp. 423-476
- dc.identifier.uri http://hdl.handle.net/10230/693
- 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.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword mc kean-vlasov equation
- dc.subject.keyword malliavin calculus
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equationca
- dc.type info:eu-repo/semantics/workingPaper