Large diffusion expansion of the transition kernel of the L\'evy Ornstein-Uhlenbeck process
Abstract
In this paper we study the L\'evy Ornstein- Uhlenbeck equation ∂t Xt=-m\,Xt+η. 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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