Hölder regularity for operator scaling stable random fields

By Hermine Bierm'e, C. Lacaux. 2007

53 citations recorded by the source corpus.

We investigate the sample path regularity of operator scaling [alpha]-stable random fields. Such fields were introduced in [H. Bierme, M.M. Meerschaert, H.P. Scheffler, Operator scaling stable random fields, Stochastic Process. Appl. 117 (3) (2007) 312-332.] as anisotropic generalizations of self-similar fields and satisfy the scaling property where E is a dxd real matrix and H>0. In the case of harmonizable operator scaling random fields, the sample paths are locally Holderian and their Holder regularity is characterized by the eigen decomposition of with respect to E. In particular, the directional Holder regularity may vary and is given by the eigenvalues of E. In the case of moving average operator scaling [alpha]-stable random fields, with [alpha][set membership, variant](0,2) and d>=2, the sample paths are almost surely discontinuous.

Subfields: Finance, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/afd1c479ae01fd38e7e1cea2bc0abfc1e0439c8e

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In Finance

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

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): “We refer to [2] and [3] for further information.”