In this paper we define semi-stable probability measures (laws) on a real separable Hilbert space and are identified as limit laws. We characterize them in terms of their Lévy-Khinchine measure and the exponent 0 p = 2. Finally we prove that every semi-stable probability measure of exponent p...

Suppose X and Y are n - 1 random vectors such that l'X + f(l) and l'Y have the same marginal distribution for all n - 1 real vectors l and some real valued function f(l), and the existence of expectations of X and Y is not necessary. Under these conditions it is proven that there exists a vector...

In this paper, a Lévy-Khintchine type representation of the characteristic function of a K-regular stable probability measure on real locally convex topological vector spaces, satisfying certain conditions, is presented.

It is established that a vector variable (X1, ..., Xk) has a multivariate normal distribution if for each Xi the regression on the rest is linear and the conditional distribution about the regression does not depend on the rest of the variables, provided the regression coefficients satisfy some...

The probability generating function (pgf) of an n-variate negative binomial distribution is defined to be [[beta](s1,...,sn)]-k where [beta] is a polynomial of degree n being linear in each si and k 0. This definition gives rise to two characterizations of negative binomial distributions. An...

The main result of this paper is the derivation of a convergence theorem for certain martingales with values in a separable Fréchet space F. It is shown that this result includes a well known theorem due to Chatterji. Moreover, the series expansion of zero-mean Gaussian elements with values in...

In applications it often occurs that the experimenter is faced with functions of random processes. Suppose, for instance, that he only can draw partial or incomplete information about the underlying process or that he has to classify events for the sake of efficiency. We assume that the...

The noncentral distributions of are obtained, where a and b are known real numbers and [theta]i's stand for latent roots of a matrix arising in each of three situations in multivariate normal theory, namely, test of equality of two covariance matrices, MANOVA, and canonical correlation. The...

It is a known fact that certain derivation bases from martingales with a directed index set. On the other hand it is also true that the strong convergence of certain abstract martingales is a consequence of the Radon-Nikodym theory for vector measures (cf. Uhl, J. J., Jr., Trans. Amer. Math....