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The Wiener-Hopf integral equation for fractional Riesz-Bessel motion

Published online by Cambridge University Press:  17 February 2009

V. V. Anh ,
W. Grecksch ,
J. M. Angulo  and
M. D. Ruiz-Medina
V. V. Anh
Affiliation:
Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia. e-mail: [email protected]
W. Grecksch
Affiliation:
Faculty of Mathematics and Informatics, Martin-Luther University of Halle-Wittenberg, D-06099, Halle, Germany. e-mail: [email protected]
J. M. Angulo
Affiliation:
Department of Statistics and Operations Research, University of Granada, Campus Fuente Nueva S/N, E-18071, Granada, Spain. e-mail: [email protected], [email protected]
M. D. Ruiz-Medina
Affiliation:
Department of Statistics and Operations Research, University of Granada, Campus Fuente Nueva S/N, E-18071, Granada, Spain. e-mail: [email protected], [email protected]
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Abstract

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This paper gives an approximate solution to the Wiener-Hopf integral equation for filtering fractional Riesz-Bessel motion. This is obtained by showing that the corresponding covariance operator of the integral equation is a continuous isomorphism between appropriate fractional Sobolev spaces. The proof relies on properties of the Riesz and Bessel potentials and the theory of fractional Sobolev spaces.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 41 - 54
Copyright
Copyright © Australian Mathematical Society 2000

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