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Estimation and filtering of fractional generalised random fields

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

J. M. Angulo ,
M. D. Ruiz-Medina  and
V. V. Anh
J. M. Angulo
Affiliation:
Departamento de Estadística e Investigación Operativa Universidad de GranadaCampus Fuente Nueva s/n E-18071 GranadaSpain e-mail: jmangulo@goliat.ugr.es
M. D. Ruiz-Medina
Affiliation:
School of Mathematical Sciences Queensland University of TechnologyGPO Box 2434 Brisbane QLD 4001Australia e-mail: v.anh@fsc.qut.edu.au
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Abstract

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This paper considers the estimation and filtering of fractional random fields, of which fractional Brownian motion and fractional Riesz-Bessel motion are important special cases. A least-squares solution to the problem is derived by using the duality theory and covariance factorisation of fractional generalised random fields. The minimum fractional duality order of the information random field leads to the most general class of solutions corresponding to the largest function space where the output random field can be approximated. The second-order properties that define the class of random fields for which the least-squares linear estimation problem is solved in a weak-sense are also investigated in terms of the covariance spectrum of the information random field.

Keywords

Wiener filteringestimation of random fieldsfractional generalised random fields

MSC classification

Secondary: 60G60: Random fields 60G20: Generalized stochastic processes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 336 - 361
Copyright
Copyright © Australian Mathematical Society 2000

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