On conditional McKean Lagrangian stochastic models

• 成果类型: Article
• 署名作者: Bossy, Mireille; Jabir, Jean-Francois; Talay, Denis
• 署名单位: Universite Cote d'Azur; Universidad de Chile
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0301-z
• 发表日期: 2011
• 页码: 319-351
• 关键词: chaos result; propagation

摘要

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.