On a class of covariance operators.
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 m-dimensional stochastic processes in Banach spaces.
In the present paper the authors prove a weak law of large numbers for multidimensional processes of random elements by means of the random weighting. The results obtained generalize those of Padgett and Taylor.
On small deviation probabilities of positive random variables.
On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets
The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian...
On some definition of expectation of random element in metric space
We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.
On the best constant in the Khinchin-Kahane inequality
We prove that if is the Rademacher system of functions then for any sequence of vectors in any normed linear space F.
On the continuity of the vector valued and set valued conditional expectations.
On the correct discrimination of Gaussian hypotheses. II.
On the definition of a probalistic normed space.
On the density of log concave seminorms on vector spaces
On the distribution of the norm for a gaussian measure
On the Itô formula in a Banach space.
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 Skorokhod topology
On the space of vector-valued functions integrable with respect to the white noise
On the tail estimation of the norm of Rademacher sums.
Operator semistable probability measures on
Operators generating p-stable measures on Banach spaces