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

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

2010-04-14

arxiv.org/abs/1004.2424v2

Physics

Mathematical Physics

12 pages, This paper has been withdrawn by the author due to a crucial sign error in page5

Scientific paper

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

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