A description of the class of semistable measures on a real separable Hilbert space is given.

Large "O" and small "o" approximations of the expected value of a class of smooth functions (f [set membership, variant] Cr(R)) of the normalized partial sums of dependent random variable by the expectation of the corresponding functions of normal random variables have been established. The same...

Let (T, , P) be a probability space, a P-complete sub-[delta]-algebra of and X a Banach space. Let multifunction t -- [Gamma](t), t [set membership, variant] T, have a [circle times operator] (X)-measurable graph and closed convex subsets of X for values. If x(t) [epsilon] [Gamma](t) P-a.e. and...

In 1937, Paul Lévy proved two theorems that characterize one-dimensional distribution functions of class L. In 1972, Urbanik generalized Lévy's first theorem. In this note, we generalize Lévy's second theorem and obtain a new characterization of Lévy probability distribution functions on...

A new technique is developed which allows to study quasimartingales with values in a Banach space E via real quasimartingales. As a byproduct path compactness for a wide class of E-valued quasimartingales is proved. The first application of this technique yields the equivalence of a.s....

The asymptotic properties of maximum likelihood estimates of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous...

The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian m-vectors. In this paper this assumption is weakened by considering a class of distributions for which the vector observations are not necessarily either...

Sobel, Uppuluri, and Frankowski, (Selected Tables in Math. Statistics, Vol. IV. Amer. Math. Soc., Providence, R. I., 1977) consider an incomplete Dirichlet integral of type I with several interesting applications connected with the multinomial distribution and provide tables of this integral...

The large sample null distribution of a progressively censored nonparametric test for multiple regression proposed by Majumdar and Sen is computed. Also the asymptotic nonnull distribution for the test based on Savage scores is computed for local alternatives when the underlying distribution is...

Convergence in probability for Toeplitz weighted sums is obtained for convex tight random elements in D[0, 1] under pointwise conditions. The almost sure convergence of the weighted sums is proved for independent, convex tight random elements and for independent, identically distributed random...