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July 2004 Large Deviations for random power moment problem
Fabrice Gamboa, Li-Vang Lozada-Chang
Ann. Probab. 32(3B): 2819-2837 (July 2004). DOI: 10.1214/009117904000000559


We consider the set Mn 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 Mn, 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 Mn on canonical moments [see the book of Dette and Studden].


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Fabrice Gamboa. Li-Vang Lozada-Chang. "Large Deviations for random power moment problem." Ann. Probab. 32 (3B) 2819 - 2837, July 2004.


Published: July 2004
First available in Project Euclid: 6 August 2004

zbMATH: 1062.60023
MathSciNet: MR2078558
Digital Object Identifier: 10.1214/009117904000000559

Primary: 30E05 , 60F10

Keywords: canonical moments , large deviations , power moment problem

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 3B • July 2004
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