The truncated milstein method for stochastic differential equations

2017/04/13 by Qian Guo, Wei Liu, Guo, Qian +5
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.04135

openalex publication_date 2017/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients

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• A note on convergence and stability of the truncated Milstein method for stochastic differential equations
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• On Milstein-Type Methods for Free Stochastic Differential Equations
• The truncated θ-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations