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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-37
Number of pages	37
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/s40072-016-0079-9
Publication status	Published - 1 Mar 2017
Externally published	Yes

Keywords

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

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10.1007/s40072-016-0079-9

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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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doi = "10.1007/s40072-016-0079-9",

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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

UR - https://www.scopus.com/pages/publications/85048219588

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DO - 10.1007/s40072-016-0079-9

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SP - 1

EP - 37

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 1

ER -

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

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Keywords

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