On the Hausdorff dimension of a set of multiple points for some stable random fields

1992 ◽  
Vol 32 (1) ◽  
pp. 54-60
Author(s):  
N. Kalinauskaitė
Keyword(s):  
Hausdorff Dimension ◽  
Random Fields ◽  
Multiple Points ◽  
Stable Random Fields

scholarly journals Sample Path Properties of Generalized Random Sheets with Operator Scaling

2020 ◽  
Author(s):  
Ercan Sönmez
Keyword(s):  
Hausdorff Dimension ◽  
Random Fields ◽  
Sample Path ◽  
Polar Coordinates ◽  
Box Counting ◽  
Sample Path Properties ◽  
Box Counting Dimension ◽  
Uniform Modulus Of Continuity ◽  
Stable Random Fields ◽  
Path Properties

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 .

scholarly journals Operator scaling stable random fields

2007 ◽  
Vol 117 (3) ◽  
pp. 312-332 ◽  
Author(s):  
Hermine Biermé ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Fields ◽  
Stable Random Fields

scholarly journals Extrapolation of stable random fields

2013 ◽  
Vol 115 ◽  
pp. 516-536 ◽  
Author(s):  
Wolfgang Karcher ◽  
Elena Shmileva ◽  
Evgeny Spodarev
Keyword(s):  
Random Fields ◽  
Stable Random Fields

scholarly journals Random tessellations associated with max-stable random fields

Bernoulli ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 30-52 ◽  
Author(s):  
Clément Dombry ◽  
Zakhar Kabluchko
Keyword(s):  
Random Fields ◽  
Random Tessellations ◽  
Stable Random Fields
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