On conditional McKean Lagrangian stochastic models

Mireille Bossy 1, * Jean Francois Jabir 1 Denis Talay 1
* Corresponding author
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : This paper 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. We study a 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, the interaction kernel is singular. We prove existence and uniqueness of the solution to the system by solving a nonlinear martingale problem and showing that the corresponding interacting particle system propagates chaos.
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Mireille Bossy, Jean Francois Jabir, Denis Talay. On conditional McKean Lagrangian stochastic models. Probability Theory and Related Fields, Springer Verlag, 2011, 151, pp.319-351. ⟨10.1007/s00440-010-0301-z⟩. ⟨inria-00345524v4⟩

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