Large deviations for random power moment problem

• 成果类型: Article
• 署名作者: Gamboa, F; Lozada-Chang, LV
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universidad de la Habana
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000559
• 发表日期: 2004
• 页码: 2819-2837
• 关键词: maximum-entropy; superresolution; inverse

摘要

We consider the set M, of all n-truncated power moment sequences of probability measures on [0, 1]. We endow this set with the uniform probability. Picking randomly a point in M, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by Chang, Kemperman and Studden [Ann. Probab. 21 (1993) 1295-1309]. Surprisingly, our large deviations results allow us to compute explicitly the (n + 1)th moment range size of the set of all probability measures having the same n first moments. The main tool to obtain these results is the representation of M, on canonical moments [see the book of Dette and Studden].