Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations - Archive ouverte HAL Access content directly
Journal Articles Stochastics and Partial Differential Equations: Analysis and Computations Year : 2017

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

Abstract

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations 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.
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Dates and versions

hal-01241704 , version 1 (10-12-2015)
hal-01241704 , version 2 (02-08-2016)

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Anthony Le Cavil, Nadia Oudjane, Francesco Russo. Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations. Stochastics and Partial Differential Equations: Analysis and Computations, 2017, 5 (1), Stochastics and partial differential equations: Analysis and Computation., vol. 5 (1), pp. 1-37, Springer-Verlag, mar, 2017. ⟨10.1007/s40072-016-0079-9⟩. ⟨hal-01241704v2⟩
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