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Operator Scaling Stable Random Fields

Hermine Biermé·Mark M. Meerschaert·Hans-Peter Scheffler
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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 H\"{o}lder-exponents and the Hausdorff-dimension of the sample paths are also obtained.

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Hermine Biermé, Mark M. Meerschaert, Hans-Peter Scheffler. 2006-02-28. Operator Scaling Stable Random Fields. https://arxiv.org/abs/math/0602664

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