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Chapitre D'ouvrage Année : 2019

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

Résumé

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 et versions

hal-02283803 , version 1 (11-09-2019)

Identifiants

Citer

Mireille Bossy, Jean-Francois Jabir. On the wellposedness of some McKean models with moderated or singular diffusion coefficient. Samuel N. Cohen; István Gyöngy; Gonҫalo dos Reis; David Siska; Łukasz Szpruch. Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, 2019, 978-3-030-22285-7. ⟨hal-02283803⟩
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