Large diffusion expansion of the transition kernel of the Lévy Ornstein-Uhlenbeck process

Abstract

In this paper we study the Lévy Ornstein- Uhlenbeck equation ${\partial }_t{X}_t=-m{X}_t+\eta$. The transition kernel of the Lévy Ornstein- Uhlenbeck process is given by a series which is not convergent in general, a large diffusion expansion of the transition kernel of the Lévy Ornstein- Uhlenbeck process will be given as well. The obtained series can be re-expressed in terms of generalized Feynman graphs and Feynman rules.

12 pages, This paper has been withdrawn by the author due to a crucial sign error in page5