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Sample Path Properties of Generalized Random Sheets with Operator Scaling

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  • Ercan Sönmez

    (University of Klagenfurt)

Abstract

We consider operator scaling $$\alpha $$ α -stable random sheets, which were introduced in Hoffmann (Operator scaling stable random sheets with application to binary mixtures. Dissertation Universität Siegen, 2011). The idea behind such fields is to combine the properties of operator scaling $$\alpha $$ α -stable random fields introduced in Biermé et al. (Stoch Proc Appl 117(3):312–332, 2007) and fractional Brownian sheets introduced in Kamont (Probab Math Stat 16:85–98, 1996). We establish a general uniform modulus of continuity of such fields in terms of the polar coordinates introduced in Biermé et al. (2007). Based on this, we determine the box-counting dimension and the Hausdorff dimension of the graph of a trajectory over a non-degenerate cube $$I \subset {\mathbb {R}}^d$$ I ⊂ R d .

Suggested Citation

  • Ercan Sönmez, 2021. "Sample Path Properties of Generalized Random Sheets with Operator Scaling," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1279-1298, September.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-020-01045-6
    DOI: 10.1007/s10959-020-01045-6
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    References listed on IDEAS

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    1. Biermé, Hermine & Lacaux, Céline, 2009. "Hölder regularity for operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2222-2248, July.
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