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Contents of PMS, Vol. 16, Fasc. 1,
pages 85 - 98
 

ON THE FRACTIONAL ANISOTROPIC WIENER FIELD

Anna Kamont

Abstract: In this paper we study the local properties of the fractional anisotropic Wiener field (B(a)(t) : t (- Rd), where a = (a ,...,a ), 1 d 0 < a < 2. i It is proved that, with probability 1, the realizations of the field B(a) over any cube Q < Rd belong to the anisotropic Hölder class with parameter a/2 in the Orlicz norm corresponding to the Young function M = exp(t2) - 1. 2 Other supporting spaces are treated as well. Moreover, the box dimension of the graph of the realization of B(a) has been calculated; it is proved that, with probability 1, the box dimension of the graph of the realization of B(a) over any cube Q < Rd is equal to d + 1- k/2, where k = min(a ,...,a ). 1 d

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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