English

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}
}
R2 v1 2026-06-21T21:21:06.051Z