Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process
AbstractWe study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox–Ingersoll–Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case, Dereich et al. (2012) have shown recently a strong convergence of order 1/2 for this scheme. Here, we obtain a strong convergence of order 1 under more restrictive assumptions on the CIR parameters.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 83 (2013)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2003.
"Asymptotic Properties of Monte Carlo Estimators of Diffusion Processes,"
CIRANO Working Papers
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- Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for non-Lipschitz SDEs," Papers 1405.3561, arXiv.org, revised Jun 2014.
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