Large deviations from the mckean-vlasov limit for weakly interacting diffusions
- 1 April 1987
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 20 (4) , 247-308
- https://doi.org/10.1080/17442508708833446
Abstract
A system of N diffusions on R$SUP:D$ESUP:in which the interaction is expressed in terms of the empirical measure is considered. The limiting behavior as N →∞ is described by a McKean_Vlasov equation. The purpose of this paper is to show that the large deviations from the McKean-Vlasov limit can be described by a generalization of the theory of Freidlin and Wentzell and to obtain a characterization of the action functional. In order to obtain this action functional we first obtain results on projective limits of large deviation systems, large deviations on dual vector spaces and a Sanov type theorem for vectors of empirical measuresKeywords
This publication has 16 references indexed in Scilit:
- Entropy, Large Deviations, and Statistical MechanicsPublished by Springer Nature ,1985
- Sanov Property, Generalized $I$-Projection and a Conditional Limit TheoremThe Annals of Probability, 1984
- Metastable behavior of stochastic dynamics: A pathwise approachJournal of Statistical Physics, 1984
- Random Perturbations of Dynamical SystemsPublished by Springer Nature ,1984
- Critical dynamics and fluctuations for a mean-field model of cooperative behaviorJournal of Statistical Physics, 1983
- Large fluctuations for a nonlinear heat equation with noiseJournal of Physics A: General Physics, 1982
- The statistics of Curie-Weiss modelsJournal of Statistical Physics, 1978
- Statistical mechanics of a nonlinear stochastic modelJournal of Statistical Physics, 1978
- Asymptotic evaluation of certain Markov process expectations for large time—IIICommunications on Pure and Applied Mathematics, 1976
- Markov ProcessesPublished by Springer Nature ,1965