南京信息工程大学学报2017，Vol.9Issue(3)：284-296,13.DOI:10.13878/j.cnki.jnuist.2017.03.006
随机微分方程数值解稳定性研究综述
Investigation on stability of numerical schemes of stochastic differential equations:A survey
摘要
Abstract
In this paper,a survey is given for the investigation on the stability of numerical schemes of stochastic differential equations in the past years.As a related topic,the convergence of the schemes is involved.The paper introduces the achieved results by literatures for the classical It(o) stochastic differential equations,stochastic functional differential equations of the neutral type, and the stochastic differential equations with Markov or Poisson jumps.The involved numerical schemes include the Euler-Maruyama scheme,the Backward Euler-Maruyama scheme,the θ scheme,and the split-step scheme,etc.The paper analyzes the academic thoughts in some classical literatures on the stability equivalence theorems and proposes some problems and challenges for further investigations on the numerical computations and simulations of stochastic differential equations at the end of the paper.关键词
随机微分方程/数值格式/稳定性/仿真Key words
stochastic differential equations/numerical schemes/stability/simulations分类
天文与地球科学引用本文复制引用
邓飞其,莫浩艺..随机微分方程数值解稳定性研究综述[J].南京信息工程大学学报,2017,9(3):284-296,13.基金项目
国家自然科学基金(61273126) （61273126）
教育部高等学校博士学科点专项科研基金(20130172110027) （20130172110027）
