On the wellposedness of some McKean models with moderated or singular diffusion coefficient
Probability
2018-09-07 v1
Abstract
We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Meleard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a weak solution using a Sobolev regularity framework instead of a Holder one. Second, we study the construction of a Lagrangian Stochastic model endowed with a conditional McKean diffusion term in the velocity dynamics and a nondegenerate diffusion term in the position dynamics.
Cite
@article{arxiv.1809.01742,
title = {On the wellposedness of some McKean models with moderated or singular diffusion coefficient},
author = {Mireille Bossy and Jean Francois Jabir},
journal= {arXiv preprint arXiv:1809.01742},
year = {2018}
}