On confined McKean Langevin processes satisfying the mean no-permeability boundary condition

Mireille Bossy 1 Jean-François Jabir 2
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 : We construct a confined Langevin type process aimed to satisfy a mean no-permeability condition at the boundary. This Langevin process lies in the class of conditional McKean Lagrangian stochastic models studied in [5]. The confined process considered here is a first construction of solutions to the class of Lagrangian stochastic equations with boundary condition issued by the so-called PDF methods for Computational Fluid Dynamics. We prove the well-posedness of the confined system when the state space of the Langevin process is a hyper-plane.
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Mireille Bossy, Jean-François Jabir. On confined McKean Langevin processes satisfying the mean no-permeability boundary condition. Stochastic Processes and their Applications, Elsevier, 2011, 121 (12), pp.2751-2775. ⟨10.1016/j.spa.2011.07.006⟩. ⟨inria-00559072v2⟩

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