Operator scaling stable random fields

By Hermine Bierm'e, Mark M. Meerschaert, Hans-Peter Scheffler. 2006

160 citations recorded by the source corpus.

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 Holder-exponents and the Hausdorff-dimension of the sample paths are also obtained.

Subfields: Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8784b70377ad6262007401bedc36ce088293864

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Yimin Xiao

In Mathematical Physics

1. C. Lacaux
2. Hermine Bierm'e
3. Yimin Xiao
4. Dongsheng Wu
5. Antoine Ayache
6. Davar Khoshnevisan

Citations in the corpus

• Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields (2009, background): “6 of [2], that is, ∀r > 0 ρ(0, rt) = rρ(0, t) with r=̂ exp(log(r)E).”
• Wavelet estimation for operator fractional Brownian motion (2015, unknown): “The study of operator self-similarity is related to that of operator stable measures (e.g., Jurek and Mason (1993) and Meerschaert and Scheffler (2001)), and of operator scaling random fields (e.g., Biermé et al. (2007), Baek et al. (2014)).”
• Characterization of Fault Roughness at Various Scales: Implications of Three-Dimensional High Resolution Topography Measurements (2008, background): “The eigenvalues of this matrix correspond to the inverse of the two roughness exponents H//, and H\ that characterize the self-affine properties of the generated surface in two perpendicular directions (BIERME et al. 2007; CLAUSEL and VEDEL, 2008).”