Strong convergence of some drift implicit Euler scheme. Application to the CIR process

Aurélien Alfonsi

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arXiv · 1206.3855

Strong convergence of some drift implicit Euler scheme. Application to the CIR process

Aurélien Alfonsi

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Abstract

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case, Dereich, Neuenkirch and Szpruch 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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Aurélien Alfonsi. 2012-06-18. Strong convergence of some drift implicit Euler scheme. Application to the CIR process. https://arxiv.org/abs/1206.3855

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