The Annals of Applied Probability

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

Fabien Panloup

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1206018192

Digital Object Identifier
doi:10.1214/105051607000000285

Mathematical Reviews number (MathSciNet)
MR2398761

Zentralblatt MATH identifier
1136.60049

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1206018192.


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