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

Anthony Le Cavil; Nadia Oudjane; Francesco Russo

doi:10.1007/s40072-016-0079-9

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

Anthony Le Cavil
, Nadia Oudjane
, Francesco Russo

Université Paris-Saclay
Laboratoire de Finance des Marchés de l’énergie

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

7 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1-37
Nombre de pages	37
journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	5
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s40072-016-0079-9
état	Publié - 1 mars 2017
Modification externe	Oui

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title = "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 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.",

keywords = "Chaos propagation, McKean type NonLinear Stochastic Differential Equation, Nonlinear Partial Differential Equations, Particle systems, Probabilistic representation of PDEs",

author = "\{Le Cavil\}, Anthony and Nadia Oudjane and Francesco Russo",

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Particle system algorithm and chaos propagation related to non-conservative mckean type stochastic differential equations. / Le Cavil, Anthony; Oudjane, Nadia; Russo, Francesco.
Dans: Stochastics and Partial Differential Equations: Analysis and Computations, Vol 5, Numéro 1, 01.03.2017, p. 1-37.

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

TY - JOUR

T1 - Particle system algorithm and chaos propagation related to non-conservative mckean type stochastic differential equations

AU - Le Cavil, Anthony

AU - Oudjane, Nadia

AU - Russo, Francesco

N1 - Publisher Copyright: © Springer Science+Business Media New York 2016.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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.

AB - 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.

KW - Chaos propagation

KW - McKean type NonLinear Stochastic Differential Equation

KW - Nonlinear Partial Differential Equations

KW - Particle systems

KW - Probabilistic representation of PDEs

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DO - 10.1007/s40072-016-0079-9

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JF - Stochastics and Partial Differential Equations: Analysis and Computations

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ER -

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

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