Representation of the characteristic function of a stochastic integral

Abstract

Let X(t) be a continuous, homogeneous stochastic process with independent increments characterized by a, σ, M, N in the Lévy representation formula. In this note we obtain the Lévy canonical representation of the characteristic function of a stochastic integral (in the sense of convergence in probability) of the form (where υ(t) is a non-decreasing, non-negative and left-continuous function) in terms of υ(t), a, σ, M, N.