A note on convergence and stability of the truncated Milstein method for stochastic differential equations

Abstract

Some new techniques are employed to release significantly the requirements on the step size of the truncated Milstein method, which was originally developed in Guo, Liu, Mao and Yue (2018). The almost sure stability of the method is also investigated. Numerical simulations are presented to demonstrate the theoretical results.

References in corpus (1)

• Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

Cited by in corpus (2)

• Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
• A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations