Matthew W. Gorr, Dane J. Youtz, Clayton M. Eichenseer, Korbin E. Smith, Timothy D. Nelin, Estelle Cormet-Boyaka, and Loren E. Wold Dorothy M. Davis Heart and Lung Research Institute, College of Medicine, The Ohio State University, Columbus, Ohio; College of Nursing, The Ohio State University, Columbus, Ohio; and Department of Veterinary Biosciences, College of Veterinary Medicine, The Ohio Stat...

On the basis of Sz. Nagy-Foia\c{s}-Langer and von Neumann-Wold decompositions, two decompositions for dissipative linear relations are given they realized by transforming invariant subspaces contractions, means Z transform. These permit separation selfadjoint completely nonselfadjoint parts a relation.

The aim of this paper to give a multidimensional version the classical one-dimensional case smooth spectral density. A density with eigenvalues and H∞ eigenvectors gives an explicit method factorize compute Wold representation weakly stationary time series. formula, similar Kolmogorov–Szego” is given for covariance matrix innovations. These results are important best linear predictions applicab...

The aim of this paper is to examine the measurement of persistence in a range of time series models nested in the framework of Cramer (1961). This framework is a generalization of the Wold (1938) decomposition for stationary time series which, in addition to accommodating the standard I(0) and I(1) models, caters for alternative nonstationary processes. Three measures of persistence are conside...

The problem that the Markov random field (MRF) model captures the structural as well as the stochastic textures for remote sensing image segmentation is considered. As the one-point clique, namely, the external field, reflects the priori knowledge of the relative likelihood of the different region types which is often unknown, one would like to consider only two-pairwise clique in the texture. ...

Stationary quantum stochastic process j is introduced as a *homomorphism embedding an involutive graded algebra K̃ = ⊕i=1Ki into a ring of (abelian) cohomologies of the one-parameter group α consisting of *-automorphisms of certain operator algebra in a Hilbert space such that every x from Ki is translated into an additive i− αcocycle j(x). It is shown that (noncommutative) multiplicative markov...

Principal components analysis is traditionally presented as an interpretive multivariate technique, where the loadings are chosen to maximally explain the variance in the variable. However, we will consider it here mainly as a statistical learning tool, by using the derived components in a least squares regression to predict unobserved response variables using the principal components. Principa...