On a. s. convergence of classes of multivalued asymptotic martingales
On Chung-Teicher type strong law for arrays of vector-valued random variables.
On complete convergence for randomly indexed sums for a case without identical distributions.
On complete convergence in a Banach space.
On complete convergence of the sum of a random number of stable type random elements.
On conditions for the strong law of large numbers in general Banach spaces.
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands.
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands. Correction.
On relatively uniform convergence of weighted sums of -lattice valued random elements
On strong laws of large numbers for arrays of rowwise independent random elements.
On subsets of and -stable processes
On the almost sure convergence of weighted sums of random elements in D(0,1).
On the bounded laws of iterated logarithm in Banach space
In the present paper, by using the inequality due to Talagrand's isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.
On the bounded laws of iterated logarithm in Banach space
In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.
On the bundle convergence of double orthogonal series in noncommutative -spaces
The notion of bundle convergence in von Neumann algebras and their -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....
On the central limit theorem in Hilbert space.
The object of this paper is to prove a central limit theorem in (separable) Hilbert space using a method based on the so called découpage de Lévy, the Lindeberg proof for the Gaussian case and an elementary proof of Poisson convergence for the direct part, and on elementary probabilistic inequalities for the converse. In particular, characteristic functions are only used in unicity questions. Several results of Varadhan (1962) can be obtained either directly as corollaries of the main theorem or...
On the conditional expectation in a regular ordered space
On the convergence of bilinear and quadratic forms in independent random variables
On the explosion of the local times along lines of brownian sheet
On the Feller strong law of large numbers for fields of -valued random variables.