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

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

36 Citations (Scopus)

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.

Original language	English
Pages (from-to)	115-135
Number of pages	21
Journal	Stochastic Processes and their Applications
Volume	84
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(99)00056-3
Publication status	Published - 1 Nov 1999

Keywords

Kac equation without cutoff
Nonlinear stochastic differential equation* Stochastic particle system

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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.",

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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

Abstract

Keywords

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