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

2012/06/18 by Aurélien Alfonsi, Alfonsi, Aurélien
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1206.3855

arxiv created 2012/06/18 · openalex publication_date 2012/06/18 · arxiv updated 2012/06/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Citations

• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

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