Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Propagation of chaos for a subcritical Keller–Segel model

David Godinho and Cristobal Quiñinao

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Abstract

This paper deals with a subcritical Keller–Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical measure of the system tends towards the unique solution of the limit equation as the number of particles goes to infinity.

Résumé

Cet article traite de l’équation de Keller–Segel dans un cadre sous-critique. À l’aide du système de particules en lien avec cette équation, nous montrons des résultats d’existence et d’unicité, puis la propagation du chaos pour ce dernier. Plus précisément, nous montrons que la mesure empirique du système tend vers l’unique solution de l’équation limite lorsque le nombre de particules tend vers l’infini.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 965-992.

Dates
Received: 20 June 2013
Revised: 13 December 2013
Accepted: 23 January 2014
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1435759237

Digital Object Identifier
doi:10.1214/14-AIHP606

Mathematical Reviews number (MathSciNet)
MR3365970

Zentralblatt MATH identifier
1342.65234

Subjects
Primary: 65C35: Stochastic particle methods [See also 82C80]

Keywords
Keller–Segel Propagation of chaos Well-posedness

Citation

Godinho, David; Quiñinao, Cristobal. Propagation of chaos for a subcritical Keller–Segel model. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 965--992. doi:10.1214/14-AIHP606. https://projecteuclid.org/euclid.aihp/1435759237


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