The Annals of Applied Probability

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

Fabien Panloup

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We study some recursive procedures based on exact or approximate Euler schemes with decreasing step to compute the invariant measure of Lévy driven SDEs. We prove the convergence of these procedures toward the invariant measure under weak conditions on the moment of the Lévy process and on the mean-reverting of the dynamical system. We also show that an a.s. CLT for stable processes can be derived from our main results. Finally, we illustrate our results by several simulations.

Article information

Ann. Appl. Probab. Volume 18, Number 2 (2008), 379-426.

First available in Project Euclid: 20 March 2008

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Zentralblatt MATH identifier

Primary: 60H35: Computational methods for stochastic equations [See also 65C30] 60H10: Stochastic ordinary differential equations [See also 34F05] 60J75: Jump processes
Secondary: 60F05: Central limit and other weak theorems

Stochastic differential equation Lévy process invariant distribution Euler scheme almost sure central limit theorem


Panloup, Fabien. Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process. Ann. Appl. Probab. 18 (2008), no. 2, 379--426. doi:10.1214/105051607000000285.

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