The truncated milstein method for stochastic differential equations

TL;DR

This paper introduces a truncated Milstein method for solving highly non-linear stochastic differential equations, demonstrating strong convergence rates close to 1 through theoretical analysis and numerical validation.

Contribution

The paper develops a truncated Milstein method with proven near-one strong convergence rate for complex stochastic differential equations, extending existing numerical techniques.

Findings

Convergence rate close to 1 for the proposed method

Theoretical proof of strong convergence

Numerical examples confirm theoretical results

Abstract

Inspired by the truncated Euler-Maruyama method developed in Mao (J. Comput. Appl. Math. 2015), we propose the truncated Milstein method in this paper. The strong convergence rate is proved to be close to 1 for a class of highly non-linear stochastic differential equations. Numerical examples are given to illustrate the theoretical results.