Strong law of large numbers for optimal points.
Strong law of large numbers under a general moment condition.
Strong laws of large numbers for arrays of rowwise conditionally independent random elements.
Strong laws of large numbers for arrays of row-wise exchangeable random elements.
Strong laws of large numbers for arrays of row-wise independent random elements.
Strong laws of large numbers for double sequences of random elements
Strong laws of large numbers for weighted sums of random elements in normed linear spaces.
Summability of double independent random variables.
Sur la convergence en moyenne pour des vecteurs aléatoires intégrables au sens de Bochner
The problem of finding simple additional conditions, for a weakly convergent sequence in , which would suffice to imply strong convergence has been widely studied in recent years. In this Note we study this problem for Banach valued random vectors, by replacing weak convergence with a less restrictive assumption. Moreover, all the additional conditions we consider are also necessary for strong convergence, and they depend only on marginal distributions.
Sur la loi du logarithme itéré dans les espaces réflexifs
Sur la propriété de la limite centrale dans
Sur le comportement asymptotique presque sûr des sommes de variables aléatoires à valeurs vectorielles
Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi
Sur l'espérance des variables aléatoires à valeurs dans les espaces de Banach réticulés
Sur l'espérance des variables aléatoires vectorielles
The Bochner mean square deviation and law of large numbers for squares of random elements in Banach lattices.
The central limit theorem for stochastic integrals.
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The invariance principle for nonstationary sequences of associated random variables
The law of large numbers, examples and counterexamples.