On conditional McKean Lagrangian stochastic models
On conditional McKean Lagrangian stochastic models
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关于条件麦基恩拉格朗日随机模型
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Talay
中科院分区：
文献类型：
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作者：
M. Bossy;Jean;D. Talay
本文的动机是一类新的SDEs-PDE系统，所谓的拉格朗日随机模型，这是常用的湍流模拟。研究了一类McKean意义下的非线性位置-速度系统。由于速度的动力学依赖于关于其位置的条件期望，因此相互作用核是奇异的。我们通过求解一个非线性鞅问题证明了系统解的存在唯一性，并证明了相应的相互作用粒子系统传播混沌。
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.