An interesting recent result of [5], Ann. Probability 5, 595-600) is investigated further. Rates of convergence in the conditioned central limit theorem are developed for partial sums and maximum partial sums, with positive mean and zero mean separately, of sequences of independent identically...

Let ([Omega], F, P) be a probability space, let H be a sub-[sigma]-algebra of F, and let Y be positive and H-measurable with E[Y] = 1. We discuss the structure of the convex set CE(Y; H) = {X [set membership, variant] pF: Y = E[XH]} of random variables whose conditional expectation given H is...

The question of existence of random solutions of nonlinear equations involving random correspondences is studied by direct use of the results from the deterministic case without resorting to iterative techniques. Applications to stochastic control and nonlinear random operator equations are given.

The correspondence between Gaussian stochastic processes with values in a Banach space E and cylindrical processes which are related to them is studied. It is shown that the linear prediction of an E-valued Gaussian process is an E-valued random variable as well as the spectral measure of an...

Let P([Theta], [tau]) || , [theta] [set membership, variant] [Theta] [subset of] , [tau] [set membership, variant] T [subset of] p denote a family of probability measures, where [tau] denotes the vector of nuisance parameters. Starting from randomized asymptotic maximum likelihood (as. m. l.)...

In the simultaneous estimation of means from independent Poisson distributions, an estimator is developed which incorporates a prior mean and variance for each Poisson mean estimated. This estimator possesses substantially smaller risk than the usual estimator in a region of the parameter space...

Through the decomposition theorem of Lebesgue and Darst it is possible to define a generalized Radon-Nikodym derivative of a bounded additive set function with respect to a bounded countably additive set function. For a bounded amart the derivatives of the components are shown to converge almost...

This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by...

The dependence concept of weak association is introduced and is shown to be equivalent to positive quadrant dependence. Furthermore, a characterization of independence in the class of positive quadrant dependent random variables by means of moment conditions is proved. Both results generalize...

A new notion of tactic for processes indexed by a directed set is introduced. The main theorem, giving conditions under which tactics can be mapped on stopping times on the line, is applied to reduce some optimal stopping problems in the plane to the same problems on the line. In the case of...