Strong convergence of some drift implicit Euler scheme. Application to the CIR process
Probability
2012-06-19 v1
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.
Cite
@article{arxiv.1206.3855,
title = {Strong convergence of some drift implicit Euler scheme. Application to the CIR process},
author = {Aurélien Alfonsi},
journal= {arXiv preprint arXiv:1206.3855},
year = {2012}
}