随机采样下随机微分方程Milstein方法的渐近误差  

Asymptotic error for the Milstein scheme for SDEs with stochastic evaluation times

作　　者：陈颖瑜[1] 张立新[1,2] 

机构地区：[1]浙江大学数学系,杭州310027 [2]浙江大学城市学院,杭州310027

出　　处：《中国科学：数学》2015年第3期287-300,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11225104);中央高校基本科研业务费资助项目

摘　　要：随机微分方程数值解的误差问题在度量离散化对冲的金融风险方面有着重要的应用.众所周知,等距采样下Ito型随机微分方程的Euler方法的收敛速度为1/n^(1/2),而Milstein方法是Euler方法的一种修正,可以将收敛速度提高到1/n,非等距、随机采样在一定程度上也能提高收敛速度.本文给出在非等距、随机采样下由一列连续局部鞅驱动的随机微分方程的Milstein方法的误差过程的渐近(弱收敛)结果.The error of the numerical solution has significant applications in measuring the risks associated with discrete hedging. It is well known that the rate of convergence of the Euler scheme approximation of the solution to It5 equations is 1/√n with equidistant evaluation times. Milstein scheme is a modification of Euler scheme to improve the rate of convergence to 1/n. In addition, using appropriate non-equidistant and stochastic evaluation times can also improve the rate. In this paper, we present the asymptotic behavior （weak convergence） of the error processes of the Milstein scheme for SDEs driven by a vector of continuous local martingales, for non-equidistant and stochastic evaluation times.

关 键 词：MILSTEIN方法 随机采样时间 平稳收敛 好性 

分 类 号：O211.63[理学—概率论与数理统计]