On confined McKean Langevin processes satisfying the mean no-permeability boundary condition (Q645593)

From the authors' summary: We construct a confined Langevin type process intended to satisfy a mean no-permeability condition at the boundary. This Langevin process lies in the class of conditional McKean Lagrangian stochastic models studied by the authors and \textit{D. Talay} [Probab. Theory Relat. Fields 151, No.~1--2, 319--351 (2011; Zbl 1234.60060)]. The confined process considered here is a first construction of solutions to the class of Lagrangian stochastic equations with boundary condition related to the so-called probability density function methods for computational fluid dynamics. We prove the well-posedness of the confined system when the state space of the Langevin process is a half-space.