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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 $L^{2} (Ω, ℱ, ℙ)$ 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 $L^{2} (Ω, ℱ, ℙ)$ ) to be orthogonal to some other sequence in $L^{2} (Ω, ℱ, ℙ)$ . The result obtained is interesting...

On a class of discrete generation interacting particle systems.

Del Moral, P., Kouritzin, M.A., Miclo, L. (2001)

Electronic Journal of Probability [electronic only]

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 Processes in Hilbert Space.

Richard Duncan (1973)

Mathematische Zeitschrift

On a class of processes with multiplicity $N = 1$ .

Mitrović, Slobodanka (1985)

Publications de l'Institut Mathématique. Nouvelle Série

On a conjecture of Kazamaki

Peter Grandits (1996)

Séminaire de probabilités de Strasbourg

On a construction of majorizing measures on subsets of ℝⁿ with special metrics

Jakub Olejnik (2010)

Studia Mathematica

We consider processes Xₜ with values in $L_{p} (Ω, ℱ, P)$ and “time” index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand’s majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.

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Oblique derivative problems and invariant measures

Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses.

Occupation times of Lévy processes as quadratic variations

On a certain class of nonstationary sequences in Hilbert space.

On a characteristic property of the asymptotic rate

On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

On a class of discrete generation interacting particle systems.

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

On a class of linear models.

On a Class of Markov Processes in Hilbert Space.

On a class of processes with multiplicity $N = 1$ .

On a conjecture of Kazamaki

On a construction of majorizing measures on subsets of ℝⁿ with special metrics

On a detection method for known finite sequences

On a formula of Pollaczek and Spitzer

On a gambler's ruin problem

On a generalization of a theorem of W. Sudderth and some applications

On a Generalization of the Cauchy Equation.

On a generalization of the martingale maximal theorem

On a Martingale Related to a Strictly Stationary Random Process in R1.

Currently displaying 1 – 20 of 392