Ben Arous, Gérard; Brunaud, Marc 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 Stochastics Stochastics Rep. 31, No. 1-4, 79-144 (1990). 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 Cited in 1 ReviewCited in 26 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60F10 Large deviations Keywords:asymptotic behaviour of diffusions; propagation of chaos; Laplace method; Gibbs variational formula Citations:Zbl 0586.60004; Zbl 0625.60025; Zbl 0572.60007; Zbl 0608.60018 PDFBibTeX XMLCite \textit{G. Ben Arous} and \textit{M. Brunaud}, Stochastics Stochastics Rep. 31, No. 1--4, 79--144 (1990; Zbl 0705.60046) Full Text: DOI