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On conditional McKean Lagrangian stochastic models
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  • Published: 26 May 2010

On conditional McKean Lagrangian stochastic models

  • Mireille Bossy1,
  • Jean-François Jabir2 &
  • Denis Talay1 

Probability Theory and Related Fields volume 151, pages 319–351 (2011)Cite this article

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  • 24 Citations

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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 with respect to 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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Authors and Affiliations

  1. INRIA Sophia Antipolis, EPI TOSCA, 2004 route des Lucioles, 06902, Sophia Antipolis Cedex, France

    Mireille Bossy & Denis Talay

  2. Center for Mathematical Modeling, Universidad de Chile, Blanco Encalada 2120, Santiago, Chile

    Jean-François Jabir

Authors
  1. Mireille Bossy
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  2. Jean-François Jabir
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  3. Denis Talay
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Corresponding author

Correspondence to Mireille Bossy.

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Cite this article

Bossy, M., Jabir, JF. & Talay, D. On conditional McKean Lagrangian stochastic models. Probab. Theory Relat. Fields 151, 319–351 (2011). https://doi.org/10.1007/s00440-010-0301-z

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  • Received: 03 July 2009

  • Revised: 25 April 2010

  • Published: 26 May 2010

  • Issue Date: October 2011

  • DOI: https://doi.org/10.1007/s00440-010-0301-z

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Keywords

  • Lagrangian stochastic model
  • Conditional McKean nonlinearity

Mathematics Subject Classification (2000)

  • 60H10
  • 60K35
  • 65C35
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