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

Author

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  • Bossy, Mireille
  • Jabir, Jean-François

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 by Bossy, Jabir and Talay (2010) [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 half-space.

Suggested Citation

  • Bossy, Mireille & Jabir, Jean-François, 2011. "On confined McKean Langevin processes satisfying the mean no-permeability boundary condition," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2751-2775.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2751-2775 DOI: 10.1016/j.spa.2011.07.006
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    References listed on IDEAS

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    1. Jorváth, Lajos & Shao, Qi-Man, 1994. "A note on the law of large numbers for directed random walks in random environments," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 275-279, December.
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