Large Deviations for Random Power Moment Problem

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We consider the set M_n 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_n, 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 \citeauthorChKS93 [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_n on canonical moments [see the book of \citeauthorDS97].
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000559

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Probability, 60F10, 30E05. (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/72788

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410175
 http://arxiv.org/abs/math/0410175
 Annals of Probability 2004, Vol. 32, No. 3B, 2819-2837
 doi:10.1214/009117904000000559

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