Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 130, Issue 2, Pages 503-520Publisher
ELSEVIER
DOI: 10.1016/j.spa.2019.01.008
Keywords
Large deviations; Empirical measure; U-statistics; Interacting particle systems; McKean-Vlasov equation; Mean-field Gibbs measure
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Funding
- CSC
- NSFC [11731009, 11571262]
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In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability condition on the negative part of the interaction potentials. In contrast to the known results we prove this without any continuity or boundedness condition on the interaction potentials. The proof relies mainly on the law of large numbers and the exponential decoupling inequality of de la Pena for U-statistics. (C) 2019 Elsevier B.V. All rights reserved.
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