Differentiable approximation of diffusion equations driven by $\alpha$-stable Lévy noise

Abstract

Edward Nelson derived Brownian motion from the Ornstein–Uhlenbeck theory by a scaling limit. Previously we extended the scaling limit to an Ornstein–Uhlenbeck process driven by an $\alpha$-stable Lévy process. In this paper we extend the scaling result to $\alpha$-stable Lévy processes in the presence of a nonlinear drift, an external field of force in physical terms.