Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process

Fabien Panloup (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a Lévy process. Our results are valid for a large class of S.D.E. that can be governed by Lévy processes with few moments or can have a weakly mean-reverting drift, and permit to find again the a.s. C.L.T for stable processes.

Mots clés: almost sure central limit theorem; stochastic differential equation; Lévy process; invariant distribution; Euler scheme; almost sure central limit theorem.

Domaines: Probabilités [math.PR]

Fabien Panloup. Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process. The Annals of Applied Probability, 2008, 18 (2), pp.379-426. ⟨hal-00009273v1⟩