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Laplace method: variational study of fluctuations of diffusions of “mean-field” type). (Méthode de Laplace: Étude variationnelle des fluctuations de diffusions de type “champ moyen”.) (French) Zbl 0705.60046

Authors’ summary: This article concerns the asymptotic behaviour of diffusions consisting of various systems of mean-field type interacting particles. Specifically we study the following properties: propagation of chaos; critical and non-critical fluctuations, using the Laplace method which has been developed by E. Bolthausen [Probab. Theory Relat. Fields 72, 305-318 (1986; Zbl 0572.60007); and ibid. 76, 167-206 (1987; Zbl 0608.60018)] in the general Banach valued random variables context; and finally the large deviations of laws of trajectorial empirical measures.
We also study Gibbs variational formula associated with this problem and show that it reduces to a finite dimensional problem.
Reviewer: B.L.S.Prakasa Rao

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60F10 Large deviations
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