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On the wellposedness of some McKean models with moderated or singular diffusion coefficient

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.

Dates and versions

hal-01869951 , version 1 (07-09-2018)

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Mireille Bossy, Jean Francois Jabir. On the wellposedness of some McKean models with moderated or singular diffusion coefficient. 2018. ⟨hal-01869951⟩
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