The Annals of Applied Probability

Propagation of chaos for interacting particles subject to environmental noise

Michele Coghi and Franco Flandoli

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Abstract

A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to the same space-dependent noise, similar to the (noninteracting) particles of the theory of diffusion of passive scalars. We prove a result of propagation of chaos and show that the limit PDE is stochastic and of inviscid type, as opposed to the case when independent noises drive the different particles.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1407-1442.

Dates
Received: March 2014
Revised: March 2015
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1465905007

Digital Object Identifier
doi:10.1214/15-AAP1120

Mathematical Reviews number (MathSciNet)
MR3513594

Zentralblatt MATH identifier
1345.60113

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35] 60K37: Processes in random environments 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Interacting particle system propagation of chaos mean field limit Kraichnan noise Wasserstain metric

Citation

Coghi, Michele; Flandoli, Franco. Propagation of chaos for interacting particles subject to environmental noise. Ann. Appl. Probab. 26 (2016), no. 3, 1407--1442. doi:10.1214/15-AAP1120. https://projecteuclid.org/euclid.aoap/1465905007


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