Convergence of Numerical Solution of The Tamed Milstein Method for NSDDEs

TL;DR

This paper introduces a tamed Milstein numerical scheme for NSDDEs with highly nonlinear coefficients, proving strong convergence under certain conditions, thus advancing numerical methods for complex stochastic delay differential equations.

Contribution

The paper develops and analyzes a tamed Milstein method specifically designed for NSDDEs with nonlinear coefficients, demonstrating its strong convergence.

Findings

The tamed Milstein scheme converges strongly to the exact solution.

Convergence is established under local Lipschitz and Khasminskii conditions.

The method effectively handles highly nonlinear coefficients in NSDDEs.

Abstract

In this paper, we apply the tamed technique to the Milstein numerical scheme to investigate Neutral Stochastic Delay Differential Equations(NSDDEs) with highly nonlinear coefficients. Under the local Lipschitz condition and Khasminskii condition, the tamed Milstein numerical solution converges strongly to the exact solution.