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

Aurélien Alfonsi

Statistics & Probability Letters, 2013, vol. 83, issue 2, 602-607

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.

Keywords: Drift implicit Euler scheme; Cox–Ingersoll–Ross model; Strong error; Lamperti transformation (search for similar items in EconPapers)
Date: 2013
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Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:602-607