Wavelet orthogonal approximation of fractional generalized random fields on bounded domains

Angulo, J.; Ruiz-Medina, M.; Anh, V.

doi:10.1090/S0094-9000-07-00677-1

Wavelet orthogonal approximation of fractional generalized random fields on bounded domains

Authors: J. M. Angulo, M. D. Ruiz-Medina and V. V. Anh
Journal: Theor. Probability and Math. Statist. 73 (2006), 1-17
MSC (2000): Primary 60G20, 60G60; Secondary 60G12, 60H40
DOI: https://doi.org/10.1090/S0094-9000-07-00677-1
Published electronically: January 17, 2007
MathSciNet review: 2213332
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Abstract: We consider a class of generalized random fields defined on bounded domains, which admit a white-noise linear filter representation in terms of linear operators of fractional order. We obtain two-sided estimates of the eigenvalues defining the pure point spectra of the associated class of covariance operators. We next derive an orthonormal basis of the reproducing kernel Hilbert space from an orthonormal basis of wavelet functions. An alternative orthogonal expansion to the Karhunen–Loève expansion is then obtained in terms of wavelet functions. The results derived can be applied to compute, in particular, the mean-square solution to fractional-order integro-differential equations, and to approximate least-squares linear estimates for the class of random fields considered.

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