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2020 Large deviations for interacting particle systems: joint mean-field and small-noise limit
Carlo Orrieri
Electron. J. Probab. 25: 1-44 (2020). DOI: 10.1214/20-EJP516

Abstract

We consider a system of stochastic interacting particles in $\mathbb {R}^{d}$ and we describe large deviation asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviation principle (LDP) is established for the empirical measure and the stochastic current, as the number of particles tends to infinity and the noise vanishes, simultaneously. We give a direct proof of the LDP using tilting and subsequently exploiting the link between entropy and large deviations. To this aim we employ consistency of suitable deterministic control problems associated to the stochastic dynamics.

Citation

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Carlo Orrieri. "Large deviations for interacting particle systems: joint mean-field and small-noise limit." Electron. J. Probab. 25 1 - 44, 2020. https://doi.org/10.1214/20-EJP516

Information

Received: 27 August 2019; Accepted: 26 August 2020; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07252705
MathSciNet: MR4150523
Digital Object Identifier: 10.1214/20-EJP516

Subjects:
Primary: 49N99, 60F10, 60H10, 60K35

JOURNAL ARTICLE
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