An application of the nonselfadjoint operators theory in the study of stochastic processes
type: Item
instance of: scholarly article
title: An application of the nonselfadjoint operators theory in the study of stochastic processes
zbMATH Open document ID: 1085.47015
DOI: 10.1155/S1048953304305034
author: L. Abbaoui
author: Latifa Debbi
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/52272
review text: In the present paper, a stochastic process is considered as a solution of an operatorial system. Using the triangular model, the correlation function of a nonstationary linearly representable stochastic process for which the corresponding operator has some specific properties is obtained. The study is made in the case when the corresponding spectrum is purely real nonconcentrated at zero. First, the case when the spectrum is concentrated at a unique point different from zero is presented. The correlation function when the spectrum is finite is obtained. In the general case, the correlation function and the infinitesimal correlated function are given as limits of sequences of correlated functions and, respectively, infinitesimal correlated functions, corresponding to a sequence of complex Gaussian stochastic processes. The result obtained here is valid for stochastic fields as well as for curves or surfaces in arbitrary Hilbert spaces.
reviewed by: Ilie Valuşescu
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 60G12
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 2166661
zbMATH Keywords: nonselfadjoint operators
zbMATH Keywords: real spectrum
zbMATH Keywords: triangular model
zbMATH Keywords: stationary processes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2166661