In this paper, the authors study a double random integral of the form [integral operator]01[integral operator]01f(s,t) M(ds) M(dt), where M(0,t) is a stable process with independent increments. Basically, the Wiener approach is used, and the existence of the above integral is established for a...

A central limit theorem for multidimensional processes in the sense of [9 and 10] is proved. In particular the asymptotic normal distribution of a sum of dependent random functions of m variables defined on the positive part of the integral lattice is established by the method of moments. The...

Let X1, ..., Xp have p.d.f. g(x12 + ... + xp2). It is shown that (a) X1, ..., Xp are positively lower orthant dependent or positively upper orthant dependent if, and only if, X1,..., Xp are i.i.d. N(0, [sigma]2); and (b) the p.d.f. of X1,..., Xp is TP2 in pairs if, and only if, In g(u) is...

Characterizations of the binomial, negative binomial, gamma, Poisson, and normal distributions are obtained by the property of zero regression of certain polynomial statistics of arbitrary degree, on the mean. In each case, the equations which express zero regression are derived from the...

Let = {Ut: t 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set (X) of all probability measures on X. By (Q; ) we denote the class of all limit measures of {Utn([mu]1 * [mu]2*...*[mu]n)*[delta]xn}, where {[mu]n}[subset, double equals]Q,...

The existence of limit spectral distribution of the product of two independent random matrices is proved when the number of variables tends to infinity. One of the above matrices is the Wishart matrix and the other is a symmetric nonnegative definite matrix.

This paper is concerned with large- error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established....

The notion of sampling for second-order q-variate processes is defined. It is shown that if the components of a q-variate process (not necessarily stationary) admits a sampling theorem with some sample spacing, then the process itself admits a sampling theorem with the same sample spacing. A...

Convergence in probability of the linear forms [Sigma]k=1[infinity] ankXk is obtained in the space D[0, 1], where (Xk) are random elements in D[0, 1] and (ank) is an array of real numbers. These results are obtained under varying hypotheses of boundedness conditions on the moments and conditions...

The problem of global estimation of the mean function [theta](·) of a quite arbitrary Gaussian process is considered. The loss function in estimating [theta] by a function a(·) is assumed to be of the form L([theta], a) = [integral operator] [[theta](t) - a(t)]2[mu](dt), and estimators are...