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

• 成果类型: Article
• 署名作者: Panloup, Fabien
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000285
• 发表日期: 2008
• 页码: 379-426
• 关键词: central limit-theorem; scheme

摘要

We study some recursive procedures based on exact or approximate Euler schemes with decreasing step to compute the invariant measure of Levy driven SDEs. We prove the convergence of these procedures toward the invariant measure under weak conditions on the moment of the Levy 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.