Probabilistic Interpretation and Numerical Approximation of a Kac Equation without Cutoff

Laurent Desvillettes; Carl Graham; Sylvie Méléard

doi:10.1016/S0304-4149(99)00056-3

Probabilistic Interpretation and Numerical Approximation of a Kac Equation without Cutoff

Laurent Desvillettes
, Carl Graham
, Sylvie Méléard

ENS Paris-Saclay
Université Paris-Nanterre

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

Résumé

A nonlinear pure-jump Markov process is associated with a singular Kac equation. This process is the unique solution in law for a nonclassical stochastic differential equation. Its law is approximated by simulable stochastic particle systems, with rates of convergence. An effective numerical study is given at the end of the paper.

langue originale	Anglais
Pages (de - à)	115-135
Nombre de pages	21
journal	Stochastic Processes and their Applications
Volume	84
Numéro de publication	1
Les DOIs	https://doi.org/10.1016/S0304-4149(99)00056-3
état	Publié - 1 nov. 1999

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10.1016/S0304-4149(99)00056-3

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title = "Probabilistic Interpretation and Numerical Approximation of a Kac Equation without Cutoff",

abstract = "A nonlinear pure-jump Markov process is associated with a singular Kac equation. This process is the unique solution in law for a nonclassical stochastic differential equation. Its law is approximated by simulable stochastic particle systems, with rates of convergence. An effective numerical study is given at the end of the paper.",

keywords = "Kac equation without cutoff, Nonlinear stochastic differential equation* Stochastic particle system",

author = "Laurent Desvillettes and Carl Graham and Sylvie M{\'e}l{\'e}ard",

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AU - Desvillettes, Laurent

AU - Graham, Carl

AU - Méléard, Sylvie

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Y1 - 1999/11/1

N2 - A nonlinear pure-jump Markov process is associated with a singular Kac equation. This process is the unique solution in law for a nonclassical stochastic differential equation. Its law is approximated by simulable stochastic particle systems, with rates of convergence. An effective numerical study is given at the end of the paper.

AB - A nonlinear pure-jump Markov process is associated with a singular Kac equation. This process is the unique solution in law for a nonclassical stochastic differential equation. Its law is approximated by simulable stochastic particle systems, with rates of convergence. An effective numerical study is given at the end of the paper.

KW - Kac equation without cutoff

KW - Nonlinear stochastic differential equation Stochastic particle system

U2 - 10.1016/S0304-4149(99)00056-3

DO - 10.1016/S0304-4149(99)00056-3

M3 - Article

AN - SCOPUS:0033228811

SN - 0304-4149

VL - 84

SP - 115

EP - 135

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Probabilistic Interpretation and Numerical Approximation of a Kac Equation without Cutoff

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