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Multivariate operator-self-similar random fields

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  • Li, Yuqiang
  • Xiao, Yimin
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    Abstract

    Multivariate random fields whose distributions are invariant under operator-scalings in both the time domain and the state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields with values in are constructed by utilizing homogeneous functions and stochastic integral representations.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-529CNSS-1/2/0bb0d9c3d1901e44b493bb2e517cf7ad
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 6 (June)
    Pages: 1178-1200

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1178-1200

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    Related research

    Keywords: Random fields Operator-self-similarity Anisotropy Gaussian random fields Stable random fields Stochastic integral representation;

    References

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    1. Tatiyana V. Apanasovich & Marc G. Genton, 2010. "Cross-covariance functions for multivariate random fields based on latent dimensions," Biometrika, Biometrika Trust, vol. 97(1), pages 15-30.
    2. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    3. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    4. Biermé, Hermine & Lacaux, Céline, 2009. "Hölder regularity for operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2222-2248, July.
    5. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
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    Cited by:
    1. Li, Yuqiang, 2011. "Fluctuation limits of site-dependent branching systems in critical and large dimensions," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1604-1611, November.

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