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

Mireille Bossy 1 Jean Francois Jabir 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
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https://hal.inria.fr/hal-01869951
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Submitted on : Friday, September 7, 2018 - 8:42:39 AM
Last modification on : Wednesday, September 11, 2019 - 11:12:08 AM

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  • HAL Id : hal-01869951, version 1
  • ARXIV : 1809.01742

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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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