参数在随机微分方程θ-Milstein方法稳定性中的影响分析  

The Effects of θ on Stability in the θ-Milstein Method for Stochastic Differential Equations

作　　者：孟雪井[1,2] 陈琳 MENG Xuejing;CHEN Lin(School of Statistics and Mathematics,Hubei University of Economics,Wuhan 430205,China;Collaborative Innovation Center of China Pilot Reform Exploration and Assessment Hubei Sub-Center Hubei University of Economics,Wuhan 430205,China;School of Statistics,Jiangxi University of Finance and Economics,Nanchang 330013,China)

机构地区：[1]湖北经济学院统计与数学学院,湖北武汉430205 [2]中国改革试点探索与评估协同创新中心湖北分中心,湖北武汉430205 [3]江西财经大学统计学院,江西南昌330013

出　　处：《应用数学》2022年第4期982-989,共8页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(11961029,11701237);the National Social Science Foundation of China(21CTJ018);the Scientific Research Project of Education Department of Hubei Province(D20212202);the Natural Science Foundation of Jiangxi Province(20202BABL201007)。

摘　　要：本文研究局部利普西茨连续系数的随机微分方程θ-Milstein方法的均方稳定性.当θ∈[0,1/2)时,一个反例显示θ-Milstein方法不能复现精确解的稳定性.通过将局部利普西茨条件略微加强一些,在θ∈[1/2,1]下,θ-Milstein方法可以得到稳定性.最后,给出一个例子验证本文的结果.We consider the mean square stability of theθ-Milstein method for stochastic differential equations with local Lipschitz continuous coefficients.Forθ∈[0,1/2),a counter example shows that theθ-Milstein method cannot reproduce the stability of the exact solution.By slightly strengthening the local Lipschitz condition,this paper concludes that theθ-Milstein method can capture the stability forθ∈[1/2,1].Finally,an example is presented to illustrate the result.

关 键 词：随机微分方程 均方稳定性 θ-Milstein方法 局部利普西茨连续 

分 类 号：O241.81[理学—计算数学]