Some confidence intervals arising from weak lp spaces

In this paper we give a method for constructing a confidence interval for the mean of certain non-square integrable random variables (r.v.). If X is such a r.v. and (X1,...,Xn) is sample of size n of X, that confidence interval involves the empirical mean Xn and the weak lp norm of the sample (the numerical constant p belonging to the interval ]1,2[).Confidence interval non-increasing rearrangement of a sequence weak lp space

Mesures majorantes et loi du logarithme itéré pour les variables aléatoires sous-gaussiennes

It is shown that for the elements X of a large class of subgaussian random variables with values in (C(S), ·[infinity]) the existence of a probability measure [lambda] on S such that: (where [psi] denotes the inverse function of x --> exp x2L2x) is sufficient to imply that X satisfies the law of the iterated logarithm.Majorizing measures law of the iterated logarithm subgaussian random variables