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

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 11. In the CIR case, Dereich et al. (2012) have shown recently a strong convergence of order 1/21/2 for this scheme. Here, we obtain a strong convergence of order 11 under more restrictive assumptions on the CIR parameters.