Operator scaling stable random fields

Hermine Biermé, Mark M. Meerschaert and Hans-Peter Scheffler

Stochastic Processes and their Applications, 2007, vol. 117, issue 3, 312-332

Abstract: A scalar valued random field is called operator-scaling if for some dxd matrix E with positive real parts of the eigenvalues and some H>0 we have where denotes equality of all finite-dimensional marginal distributions. We present a moving average and a harmonizable representation of stable operator scaling random fields by utilizing so called E-homogeneous functions [phi], satisfying [phi](cEx)=c[phi](x). 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.

Keywords: Fractional; random; fields; Operator; scaling (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (22)

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