Operator Scaling Stable Random Fields

Abstract : A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions. These fields also have stationary increments and are stochastically continuous. In the Gaussian case critical Hölder-exponents and the Hausdorff-dimension of the sample paths are also obtained.
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Contributor : Hermine Biermé <>
Submitted on : Tuesday, February 28, 2006 - 2:44:29 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
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Hermine Biermé, Mark Meerschaert, Hans-Peter Scheffler. Operator Scaling Stable Random Fields. Stochastic Processes and their Applications, Elsevier, 2007, 117 (3), pp.312-332. ⟨10.1016/j.spa.2006.07.004⟩. ⟨hal-00019844⟩

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