Strong convergence rates for Cox–Ingersoll–Ross processes — Full parameter range

• Published in: Journal of mathematical analysis and applications Vol. 459; no. 2; pp. 1079 - 1101
• Main Authors: Hefter, Mario, Herzwurm, André
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.03.2018
• Subjects: Cox–Ingersoll–Ross process; Milstein-type scheme; Square root diffusion coefficient; Squared Bessel process; Strong approximation; Strong approximation; Square root diffusion coefficient; Milstein-type scheme; Cox–Ingersoll–Ross process; Squared Bessel process
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2017.10.076

We study strong (pathwise) approximation of Cox–Ingersoll–Ross processes. We propose a Milstein-type scheme that is suitably truncated close to zero, where the diffusion coefficient fails to be locally Lipschitz continuous. For this scheme we prove positive convergence rates for the full parameter range including the accessible boundary regime. The error criterion is given by the maximal Lp-distance of the solution and its approximation on a compact interval. In the particular case of a squared Bessel process of dimension δ>0 the convergence rate is given by min⁡(1,δ)/(2p).