Sample Path Properties of Generalized Random Sheets with Operator Scaling

Ercan Sönmez ()
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Ercan Sönmez: University of Klagenfurt

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1279-1298

Abstract: 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 .

Keywords: Fractional random fields; Stable random sheets; Operator scaling; Selfsimilarity; Box-counting dimension; Hausdorff dimension; Primary 60G60; Secondary 28A78; 28A80; 60G17; 60G52 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01045-6

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