English

Large diffusion expansion of the transition kernel of the L\'evy Ornstein-Uhlenbeck process

Mathematical Physics 2011-04-11 v2 math.MP

Abstract

In this paper we study the L\'evy Ornstein- Uhlenbeck equation tXt=mXt+η\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.

Keywords

Cite

@article{arxiv.1004.2424,
  title  = {Large diffusion expansion of the transition kernel of the L\'evy Ornstein-Uhlenbeck process},
  author = {Boubaker Smii},
  journal= {arXiv preprint arXiv:1004.2424},
  year   = {2011}
}

Comments

12 pages, This paper has been withdrawn by the author due to a crucial sign error in page5