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On a characterization of orthogonality with respect to particular sequences of random variables in L 2

Umberto Triacca, Andrei Volodin (2010)

Applications of Mathematics

This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space L 2 ( Ω , , ) of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of L 2 ( Ω , , ) ) to be orthogonal to some other sequence in L 2 ( Ω , , ) . The result obtained is interesting...

On a class of estimators in a multivariate RCA(1) model

Zuzana Prášková, Pavel Vaněček (2011)

Kybernetika

This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...

On a class of linear models.

Radu Theodorescu (1985)

Trabajos de Estadística e Investigación Operativa

This paper is concerned with classification criteria, asymptotic behaviour and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. This problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation...

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

Studia Mathematica

We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.

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