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arXiv · 1004.2424

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

Boubaker Smii
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Abstract

In this paper we study the Lévy Ornstein- Uhlenbeck equation $\partial_t X_t=-m\,X_t+η$. 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.

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Boubaker Smii. 2011-04-08. Large diffusion expansion of the transition kernel of the Lévy Ornstein-Uhlenbeck process. https://arxiv.org/abs/1004.2424

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