Open Access
April 2008 Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process
Fabien Panloup
Ann. Appl. Probab. 18(2): 379-426 (April 2008). DOI: 10.1214/105051607000000285

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.

Citation

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Fabien Panloup. "Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process." Ann. Appl. Probab. 18 (2) 379 - 426, April 2008. https://doi.org/10.1214/105051607000000285

Information

Published: April 2008
First available in Project Euclid: 20 March 2008

zbMATH: 1136.60049
MathSciNet: MR2398761
Digital Object Identifier: 10.1214/105051607000000285

Subjects:
Primary: 60H10 , 60H35 , 60J75
Secondary: 60F05

Keywords: Almost sure Central Limit Theorem , Euler scheme , Invariant distribution , Lévy process , Stochastic differential equation

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.18 • No. 2 • April 2008
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