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Wavelet-vaguelette decomposition of spatiotemporal random fields |
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| Authors: | M. D. Ruiz-Medina J. M. Angulo R. Fernández-Pascual |
| Affiliation: | (1) Departamento de Estadística e Investigación Operativa, Universidad de Granada, Campus de Fuente Nueva s/n, 18071 Granada, Spain;(2) Departamento de Estadística e Investigación Operativa, Universidad de Jaén, Campus Las Lagunillas s/n, 23071 Jaén, Spain |
| Abstract: | A wavelet-based orthogonal decomposition of the solution to stochastic differential/pseudodifferential equations of parabolic type is derived in the cases of random initial conditions and random forcing. The family of spatiotemporal models considered can represent anomalous diffusion processes when the spatial operator involved is a fractional or multifractional pseudodifferential operator. The results obtained are applied to the generation of the sample paths of Gaussian spatiotemporal random fields in the family studied. |
| Keywords: | Anomalous diffusion processes Orthogonal expansions Spatiotemporal random fields Stochastic evolution equations Wavelets |
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