Characteristic function for the stationary state of a one-dimensional dynamical system with Lévy noise

We develop a practical method for calculating the characteristic function of diffusion processes driven by Lévy white noise. The method is based on the Itô formula for semimartingales, a differential equation developed for the characteristic function of diffusion processes driven by Poisson white noise with jumps that may not have finite moments, and on approximate representations of the Lévy white noise process. Numerical results show that the proposed method is very accurate and is consistent with previous theoretical findings.