Fractional Lévy processes on Gel’fand triple and stochastic integration

Abstract

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel'fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.

A white noise approach to stochastic partial differential equations driven by the fractional Lévy noise

“…In [14], the authors defined a stochastic integral for a class of deterministic integrands with respect to real-valued fractional Lévy processes. In [13], we defined a stochastic integral for a class of real deterministic functions and deterministic operator-valued processes with respect to fractional Lévy processes on Gel'fand triple. In [1], by using Stransform the authors investigated the Skorokhod integral for fractional Lévy processes whose underlying Lévy processes have finite moments of any order by avoiding Malliavin calculus and white noise analysis.…”

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

“…By the Riemann-Liouville fractional integral, Huang et al [10] defined the fractional Lévy processes and noises on a Gel'fand triple and investigated their distribution properties. Lü et al [12] further investigated the distribution properties of fractional Lévy processes on a Gel'fand triple restricted to the case that the underlying Lévy processes are centered and square integrable, and defined the stochastic integration with respect to the fractional Lévy processes for deterministic integrands.…”