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On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient
Ch. 2. P. 43–87.
Jabir J. M., Bossy M.
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 Méléard 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 Hölder 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.