On conditional McKean Lagrangian stochastic models
Résumé
This work is devoted to the well-posedness of a particle position--velocity system which is nonlinear in the sense of McKean. As the dynamics of the velocity depends on the conditional expectation w.r.t. its position, we have to deal with a singular interaction kernel between particles. This study is motivated by a new class of SDEs--PDEs systems, the so called Lagrangian stochastic models which are commonly used in the simulation of turbulent flows. After a short presentation of these systems, we prove existence and uniqueness results for a simplified model, and a propagation of chaos result for the corresponding interacting particle system.
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