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.
The law of the iterated logarithm for a triangular array of empirical processes.
Théorème limite central dans les espaces
Topologie faible et méta-stabilité