Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Nonlinear martingale problems involving singular integrals


Code(s) de Classification MSC:

Résumé: We study a class of nonlinear martingale problems in one dimension, that involve a singular integral of the density in the drift term, and are related to systems of particles with singular interactions. First we prove existence and uniqueness of regular solutions of the associated nonlinear evolution equation. Then, we establish a suitable framework and conditions where the martingale problem is well posed. This extends the results of Bonami, Bouchut, C\'epa and L\'epingle \cite{BBCL} to a wide class of coefficients and initial conditions. Finally, we obtain our solution of the martingale problem as the chaotic limit of some systems of particles interacting through regular approximating kernels.

Mots Clés: McKean-Vlasov equation ; singular integrals ; nonlinear martingale problem ; Monte Carlo approximation

Date: 2002-03-27

Prépublication numéro: PMA-718

Pdf file : PMA-718.pdf