FRACTIONAL LÉVY PROCESSES AND NOISES ON GEL′FAND TRIPLE

Abstract

In this paper, we construct a class of infinitely divisible distributions on Gel′fand triple. Based on this construction, we define Lévy processes on Gel′fand triple and give their Lévy–Itô decompositions. Then, we construct the general Lévy white noises on Gel′fand triple. By using the Riemann–Liouville fractional integral method, we define the general fractional Lévy noises on Gel′fand triple and investigate their distribution properties.