Skip to main content
SpringerLink
Log in

Wavelet-vaguelette decomposition of spatiotemporal random fields

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Adler RJ, Feldman RE, Taqqu MS (1992) A practical guide to heavy tails: statistical techniques and applications (Birkhäuser 1992)

  • Angulo JM, Ruiz-Medina MD (1999) Multiresolution approximation to the stochastic inverse problem. Adv App Prob 31:1039–1057

    Article  Google Scholar 

  • Angulo JM, Ruiz-Medina MD, Anh VV (2004) Wavelet orthogonal approximation of fractional generalized random fields on bounded domains. Theor Prob Math Stat 71:28–43

    Google Scholar 

  • Bardet J, Lang G, Moulines E, Soulier P (2000) Wavelet estimator of long range dependence processes. Stat Infer Stoch Proc 31:85–99

    Article  Google Scholar 

  • Christakos G (2000) Modern spatiotemporal geostatistics. Oxford University Press, Oxford

  • Donoho DL (1995) Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl Comput Harmonic Anal 2:101–126

    Article  Google Scholar 

  • Fernández-Pascual R, Ruiz-Medina MD, Angulo JM (2004) Wavelet-based functional reconstruction and extrapolation of fractional random fields. Test 13:417–444

    Article  Google Scholar 

  • Jensen MJ (2000) An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets. J Econom Dynam Contr 24:361–387

    Article  Google Scholar 

  • Leduc JP (1997) Spatiotemporal wavelet transforms for digital signal analysis. Sign Proc 60:23–41

    Article  Google Scholar 

  • Ruiz-Medina MD, Angulo JM (2002) Spatiotemporal filtering using wavelets. Stoch Environm Res Risk Assess 16:241–266

    Article  Google Scholar 

  • Ruiz-Medina MD, Angulo JM, Anh VV (2003) Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields. J Multiv Anal 85:192–216

    Article  Google Scholar 

  • Shafri HZM, Mather PM (2005) Wavelet shrinkage in noise removal of hysperspectral remote sensing data. Amer J Appl Sci 2:1169–1173

    Article  Google Scholar 

  • Wikle CK (2003) Spatio temporal methods in climatology. Encyclopedia of Life Support Systems (EOLSS 2003)

  • Wong E, Hajek B (1985) Stochastic processes in engineering systems. Springer, Berlin Heidelberg New York

  • Yuen DA, Garbow ZA, Erlebacher G (2004) Remote data analysis, visualization and problem solving environment (PSE) based on wavelets in the geosciences. Vis Geosci 8:83–92

    Google Scholar 

Download references

Acknowledgments

This work has been supported in part by projects MTM2005-08597 of the DGI, MEC, and P05-FQM-00990 of the Andalousian CICE, Spain.

Author information

Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Granada, Campus de Fuente Nueva s/n, 18071, Granada, Spain

    M. D. Ruiz-Medina & J. M. Angulo

  2. Departamento de Estadística e Investigación Operativa, Universidad de Jaén, Campus Las Lagunillas s/n, 23071, Jaén, Spain

    R. Fernández-Pascual

Authors
  1. M. D. Ruiz-Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Angulo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Fernández-Pascual
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. D. Ruiz-Medina.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruiz-Medina, M.D., Angulo, J.M. & Fernández-Pascual, R. Wavelet-vaguelette decomposition of spatiotemporal random fields. Stoch Environ Res Ris Assess 21, 273–281 (2007). https://doi.org/10.1007/s00477-006-0062-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-006-0062-5

Keywords

Search

Navigation