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On the orthogonal representation of generalized random fields

Author

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  • Angulo, J. M.
  • Ruiz-Medina, M. D.

Abstract

An orthogonal representation for a class of generalized random fields defined on an infinite-dimensional separable Hilbert space is studied. This representation is an extension of the expansion studied in Ruiz-Medina and Angulo (1995). The results are applied to obtain the orthogonal expansion for a linear functional of a zero-mean, second-order random field satisfying certain regularity conditions. Finally, some applications of the above representation in obtaining linear prediction estimates, and in obtaining explicit-form solutions to stochastic partial differential equations, are discussed.

Suggested Citation

  • Angulo, J. M. & Ruiz-Medina, M. D., 1997. "On the orthogonal representation of generalized random fields," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 145-153, January.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:3:p:145-153
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    Cited by:

    1. Medina, Juan Miguel & Frías, Bruno Cernuschi, 2005. "On the a.s. convergence of certain random series to a fractional random field in," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 39-49, August.
    2. Ruiz-Medina, M. D. & Angulo, J. M. & Anh, V. V., 2003. "Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 192-216, April.

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