Wavelet-Based Functional Reconstruction and Extrapolation of Fractional Random Fields

• Autores: Rosaura Fernández Pascual , María Dolores Ruiz Medina , José Miguel Angulo Ibáñez
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 13, Nº. 2, 2004, págs. 417-444
• Idioma: inglés
• DOI: 10.1007/bf02595780
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• Resumen

  • Least-squares linear functional reconstruction and extrapolation of a random field defining the random input of a linear system represented by an integral equation is considered. This problem is solved for a class of random fields with reproducing kernel Hilbert space norm equivalent to the norm of a Sobolev space of an appropriate fractional order. More specifically, functional reconstruction and extrapolation formulae are derived from generalized wavelet-based orthogonal expansions of the input and output random fields in the class considered (see Angulo and Ruiz-Medina, 1999, for the ordinary case). In the Gaussian and ordinary case, the results derived also provide sample-path functional reconstruction and extrapolation formulae. Simulation studies are carried out for systems defined in terms of fractional integration of fractional Brownian motion.