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

2010/04/14 by Boubaker Smii, Smii, Boubaker
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G20 #60H10 #81T15 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1004.2424

openalex publication_date 2010/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Lévy Ornstein- Uhlenbeck equation ∂_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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