Three types of series representations are considered for Hilbert space valued second-order stochastic processes over the real line. These are called ordinary, modular, and tensor series representations. Relations among these representations are given in connection with the separability of the...

The concept of the mean remaining life function is extended to the multivariate case. Some general characterization properties of multivariate mean remaning life functions (mmrl) are studied, it is shown that they determine the joint pdf uniquely. Inter alia a basic convergence result is proved...

In univariate calibration problems two different estimators are commonly in use. They are referred to as the classical estimator and the inverse estimator. [8], Technometrics 9, No. 3 425-439) compared these two methods of calibration by means of an extensive Monte Carlo study. Without...

Stationary vector ARMA processess x(t), t = 0, ±1, ±2,..., that are full rank are considered. It is shown, with E(z) denoting the 'symbol' of the canonical correlation operator, that the number of zeros (counting multiplicities) on z = 1 of the transfer function, V(z), from innovations to...

It is shown that paradoxes arise in conditional probability calculations, due to incomplete specification of the problem at hand. This is illustrated with the Borel and the Kac-Slepian type paradoxes. These are significant in applications including Bayesian inference. Also Rényi's axiomatic...

Bounds on the norming operators for distributions in the domain of attraction of an operator-stable distribution are found. These bounds are used to establish the existence and nonexistence of moments of distributions in the domain of attraction of an operator-stable distribution. Similar...

In this paper we formulate and prove a general principle which enables us to deduce limit theorems for a sequence of random variables on a finitely additive probability space.

The area of the largest circle around the origin completely covered by a simple symmetric plane random walk is investigated.

In [3]. J. Appl. Probab.4, in press) a very general cost mechanism for a maintained system was considered. There he established a relationship between the expected long run cost per unit time for the age and block maintenance policies. In the present paper a similar relationship is obtained for...

We describe a unified approach to the construction of confidence bands in nonparametric density estimation and regression. Our techniques are based on interpolation formulae in numerical differentiation, and our arguments generate a variety of bands depending on the assumptions one is prepared...