Generalized fractional Lévy random fields on Gel’fand triple: A white noise approach

Abstract

In this paper, under the first-order moment condition of the infinitely divisible distribution on Gel’fand triple, we use Riesz potential to construct fractional Lévy random fields on Gel’fand triple by white noise approach. We investigate the distribution and sample properties of isotropic and anisotropic fractional Lévy random fields, respectively.

Keywords

Infinitely divisible distributions / Gel’fand triple / fractional Lévy noise / generalized Lévy random field / fractional generalized Lévy random field / anisotropic Lévy random fields

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