On the Mean of a Stochastic Integral with Non-Gaussian α-Stable Noise.

In this article, we consider a Levy process under condition Γ1 = x where {Γk} is a sequence of arrivals of a Poisson process with unit arrival rate. We show that under condition Γ1 = x Levy process can be decomposed into a simple process and a Levy process. These two processes are independent. As an application of this decomposition we consider α-stable Levy processes. We give a closed form of the process [image omitted] and evaluate its expected value where Z is an α-stable Levy process with 0 < α < 2. We show that X(t) = 0 for 1 < α < 2 and this expectation is equal infinity for α ≤ 1. [ABSTRACT FROM AUTHOR]