On the Feller strong law of large numbers for fields of -valued random variables.
On the local limit theorem for general lattice distribution.
On the moments of sums of independent identically distributed random variables.
On the negative dependence in Hilbert spaces with applications
This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.
On the rate of convergence of bootstrapped means in a Banach space.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the strong law for arrays and for the bootstrap mean and variance.
Pointwise limit theorem for a class of unbounded operators in -spaces
We distinguish a class of unbounded operators in , r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in -spaces are applied.
Quelques théorèmes ergodiques dans les espaces
Random Fourier Series with Respect to a General Orthonormal System in L...(..) Spaces.
Remarks on stable measures on Banach spaces
Sample behavior and laws of large numbers for Gaussian random elements.
Some comments on a result of Hanš on strong convergence of sequences of random elements in separable Banach spaces
Some recent results on the law of the iterated logarithm for Banach space valued random variables
Some results on convergence rates for probabilities of moderate deviations for sums of random variables.
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes
Some results on the convergence of weighted sums of random elements in separable Banach spaces
Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree.
Some special cases of a general convergence rate theorem in the law of large numbers.
Stability for randomly weighted sums of random elements.