Large Deviations of U-Empirical Measures in Strong Topologies and Applications

Peter Eichelsbacher and Uwe Schmock

Abstract: We prove large deviation principles (LDP) for m-fold products of empirical measures and for U-empirical measures, where the underlying i.i.d. random variables take values in a measurable (not necessarily Polish) space S. The results can be formulated on suitable subsets of all probability measures on the product space Sm. We endow the spaces with topologies, which are stronger than the usual tau-topology and which make integration with respect to certain unbounded, Banach-space valued functions a continuous operation. A special feature is the non-convexity of the rate function for m>2. Improved versions of LDPs for Banach-space valued U- and V-statistics are obtained as a particular application. Some further applications concerning the Gibbs conditioning principle and a process level LDP are mentioned.

Keywords: large deviations, empirical measures, Sanov's theorem, strong topology, U-statistics, von Mises statistics, Gibbs conditioning principle, mean-field model, process-level large deviations

Reference: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 38, No. 5 (2002) 779-797.

DOI: 10.1016/S0246-0203(02)01116-0

2010 Mathematics Subject Classification:

The paper (16 pages, revised version February 18, 2002) is available in:

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