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Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

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  • Alfonsi, Aurélien
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    Abstract

    We 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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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004063
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 602-607

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:602-607

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    Related research

    Keywords: Drift implicit Euler scheme; Cox–Ingersoll–Ross model; Strong error; Lamperti transformation;

    References

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    1. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2003. "Asymptotic Properties of Monte Carlo Estimators of Diffusion Processes," CIRANO Working Papers 2003s-11, CIRANO.
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    Cited by:
    1. 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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