Computation of the invariant measure for a Lévy driven SDE: Rate of convergence

Fabien Panloup (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a Lévy process. The main interest of this work is to compare the rates induced by exact and approximate Euler schemes. In our main result, we show that replacing the small jumps by a Brownian component in the approximate case preserves the rate induced by the exact Euler scheme for a large class of Lévy processes.

Mots clés: stochastic differential equation; Lévy process; invariant distribution; Euler scheme; rate of convergence.; rate of convergence

Domaines: Probabilités [math.PR]

Fabien Panloup. Computation of the invariant measure for a Lévy driven SDE: Rate of convergence. Stochastic Processes and their Applications, 2008, 118 (8), pp.1351-1384. ⟨hal-00111101⟩