Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations

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• 作者：Anthony Le Cavil ; Nadia Oudjane…
• 关键词：Chaos propagation ; Nonlinear Partial Differential Equations ; McKean type NonLinear Stochastic Differential Equation ; Particle systems ; Probabilistic representation of PDEs
• 刊名：Stochastics and Partial Differential Equations: Analysis and Computations
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：5
• 期：1
• 页码：1-37
• 全文大小：
• 刊物主题：Probability Theory and Stochastic Processes; Partial Differential Equations; Statistical Theory and Methods; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Nu
• 出版者：Springer US
• ISSN：2194-041X
• 卷排序：5

文摘

We discuss numerical aspects related to a new class of NonLinear Stochastic Differential Equation (NLSDE) in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential Equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE.