Stabilité de sommes pondérées de variables aléatoires vectorielles

Jean-Christian Alt

Journal of Multivariate Analysis, 1989, vol. 29, issue 1, 137-154

Abstract: Stochastic convergence and almost sure convergence are studied for weighted sums Sn = [Sigma]k = 1kn ankXk of random variables taking values in a Banach space B. These convergence properties are obtained under various regularity assumptions on the sequence (Xn). For instance, the following set of hypotheses is put on the random variables (Xn): (i) [Sigma]k = 1kn ank[alpha] [infinity]supk=1knank = 0; (iii) lims-->[infinity]supnsupt [greater-or-equal, slanted]- s t[alpha]P[[short parallel]Xn[short parallel] >= t] = 0; (iv) B is of [alpha]-stable type.

Keywords: strong; law; of; large; numbers; weak; law; of; large; numbers; Banach; spaces; of; stable; type (search for similar items in EconPapers)
Date: 1989
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