Large Deviations on Moment Spaces

Li-Vang Lozada-Chang (Université Paul Sabatier, France)

Abstract


In this paper we study asymptotic behavior of some moment spaces. We consider two different settings. In the first one, we work with ordinary multi-dimensional moments on the standard $m$-simplex. In the second one, we deal with the trigonometric moments on the unit circle of the complex plane. We state large and moderate deviation principles for uniformly distributed moments. In both cases the rate function of the large deviation principle is related to the reversed Kullback information with respect to the uniform measure on the integration space.

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Pages: 662-690

Publication Date: July 1, 2005

DOI: 10.1214/EJP.v10-202

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