Strong convergence order and stochastic C-stability of the projected Milstein method for stochastic delay differential equations with non-globally Lipschitz continuous coefficients
Abstract
This paper presents the first rigorous proof that a strong convergence rate of order one can be achieved for numerical methods solving stochastic delay differential equations under non-global Lipschitz conditions. A projected Milstein method is introduced for stochastic delay differential equations with a constant delay. Under local Lipschitz and coupled drift-diffusion conditions, the C-stability and B-consistency of the proposed method are established, leading to strong convergence of order one in the mean-square sense. A numerical experiment is conducted to validate the theoretical results, confirming the efficacy and accuracy of the method.
Fields of Study & Subjects
Stochastic processes and financial applications
Stochastic Gradient Optimization Techniques
Risk and Portfolio Optimization
Publication details
- Journal / source
- International Journal of Computer Mathematics
- Publisher
- Informa UK Limited
- Volume
- 103
- Issue
- 10
- Pages
- 1–21
- Publication date
- 21 April 2026
- Language
- EN