We give a complete characterization of a class of quantum stochastic processes with independent, stationary increments. We prove that processes of the class are, up to a canonical equivalence, equal to a sum of creation, second quantization, annihilation, and scalar processes on a Bose/Fermi...

Let Xi, Yj, and Zij (i, j [set membership, variant] Z+) be independent families of i.i.d. random variables uniformly distributed on [0, 1], and let 0 p 2. We obtain conditions on a Borel function f defined on [0, 1]3 such that thus extending a result due to McConnell and Rieders when p = 1....

We obtain limit theorems for sup [alpha]n(t,s)/(t[lambda]s[mu]G(t)L(s)), where [alpha]n is the bivariate uniform empirical process, , , and G, L are slowly varying functions at zero.

Tests for comparing a multivariate response on a control and on a treatment population are considered. It is assumed that each component of the response is a categorical variable with ordered categories. In some situations it may be believed a priori that the treatment has a nondecreasing effect...

We obtain a unform strong approximation for the distribution of a Nadaraya-Watson kernel estimator of a regression function. The approximation is obtained for general multivariate explanatory variables under an algebraic moment condition on the errors. A stronger rate of convergene result for...

Let (Z1,M1),..., (Zn,Mn) be independent and identically distributed 1 - (p + 1) random vectors from the exponential-multinomial distribution which has density function f(z,m[theta]) = [lambda] exp(-[lambda]z) [Pi]j=1p([theta]j/[lambda])mj for z 0 and m = (m1,...,mp) with mj [set membership,...

A Cramér-Rao type lower bound for minimum loss unbiased estimators with values in a manifold is derived, and the corresponding notion of efficiency is investigated. A by-product is a generalisation of the concept of covariance of a multivariate statistic to one of a statistic with values in a...

This paper studies the sample path properties of stochastic processes represented by multiple symmetric [alpha]-stable integrals. It relates the "smoothness" of the sample paths to the "smoothness" of the (non-random) integrand. It also contains results about the behavior of the distribution of...

A large number of characterizations of univariate exponential distributions are known; these often lead to a functional equation, relatively few of which have been extended to the multivariate case. This paper is an exposition of multivariate extensions and relatives of the functional equation...

Scott, Freedman, and Diaconis derived expressions for optimal interval widths in fixed-interval univariate histograms and Terrell and Scott obtained corresponding results for variable-interval univariate histograms. The present paper considers the more general problem of optimal fixed and...