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January 2012 Large deviation properties of weakly interacting processes via weak convergence methods
Amarjit Budhiraja, Paul Dupuis, Markus Fischer
Ann. Probab. 40(1): 74-102 (January 2012). DOI: 10.1214/10-AOP616

Abstract

We study large deviation properties of systems of weakly interacting particles modeled by Itô stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean–Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay.

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Amarjit Budhiraja. Paul Dupuis. Markus Fischer. "Large deviation properties of weakly interacting processes via weak convergence methods." Ann. Probab. 40 (1) 74 - 102, January 2012. https://doi.org/10.1214/10-AOP616

Information

Published: January 2012
First available in Project Euclid: 3 January 2012

zbMATH: 1242.60026
MathSciNet: MR2917767
Digital Object Identifier: 10.1214/10-AOP616

Subjects:
Primary: 60F10 , 60K35
Secondary: 34K50 , 60B10 , 60H10 , 93E20

Keywords: Delay , Interacting random processes , large deviations , Martingale problem , McKean–Vlasov equation , optimal stochastic control , Stochastic differential equation , weak convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 1 • January 2012
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