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Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure

Author

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  • Lim, S.C.
  • Teo, L.P.

Abstract

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.

Suggested Citation

  • Lim, S.C. & Teo, L.P., 2009. "Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1325-1356, April.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1325-1356
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    References listed on IDEAS

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    1. Gneiting T., 2002. "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 590-600, June.
    2. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    3. Gabriel Lang & François Roueff, 2001. "Semi-parametric Estimation of the Hölder Exponent of a Stationary Gaussian Process with Minimax Rates," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 283-306, October.
    4. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    5. S. Davies & P. Hall, 1999. "Fractal analysis of surface roughness by using spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 3-37.
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    Cited by:

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