Fractional generalized Lévy random fields as white noise functionals

Abstract

In this paper, we construct the fractional generalized Lévy random fields (FGLRF) as tempered white noise functionals. We find that this white noise approach is very effective in investigating the properties of these fields. Under some conditions, the fractional Lévy fields in the usual sense are obtained. In addition, we also present a method to construct the anisotropic fractional generalized Lévy random fields (AFGLRF).

Keywords

Riesz potential / tempered Lévy white noise / fractional generalized random field / anisotropic random field

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