Large Deviations for Random Power Moment Problem

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].Comment: 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/10.1214/00911790400000055

Generalized Dirichlet distributions on the ball and moments

The geometry of unit $N$-dimensional $\ell_{p}$ balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest, such questions have applications in several probabilistic and geometric contexts (Barthe et al. 2005). In this paper, our aim is to revisit some known results of this flavour with a new point of view. Roughly speaking, we will endow the ball with some kind of Dirichlet distribution that generalizes the uniform one and will follow the method developed in Skibinsky (1967), Chang et al. (1993) in the context of the randomized moment space. The main idea is to build a suitable coordinate change involving independent random variables. Moreover, we will shed light on a nice connection between the randomized balls and the randomized moment space.Comment: Last section modified. Article accepted by ALE

A toolbox on the distribution of the maximum of Gaussian process

In this paper we are interested in the distribution of the maximum, or the maximum of the absolute value, of certain Gaussian processes for which the result is exactly known

Asymptotics of Random moment vectors and empirical variance matrices (applications)

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF

On functional quantization of gaussian process

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF

Asymptotic behavior of moment sequences

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 22522, issue : a.2004 n.4 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Large deviations for random power moment problem

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 22522, issue : a.2003 n.3 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc