带分数Brown运动和局部线性增长的随机微分方程  

SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth

作　　者：冉启康 Ran Qikang(College of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433)

机构地区：[1]上海财经大学数学学院,上海200433

出　　处：《数学物理学报（A辑）》2020年第1期200-211,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601306)。

摘　　要：该文讨论了一类带分数Brown运动,且系数为局部线性增长的随机微分方程适应解的存在唯一性.使用一种广义tieltjes积分定义方法定义关于分数Brown运动的随机积分,利用这种积分的性质,得到了一类由标准Brown运动和一个Hurst指数H∈(1/2,1)的分数Brown运动共同驱动的、系数为局部线性增长的随机微分方程适应解的存在唯一性结果.In this paper,we discuss the existence and uniqueness of a class of stochastic differential equations driven by fractional Brown motion with Hurst parameter H∈(1/2,1)and their coefficients are local linear growth.So far,there are several ways to define stochastic integrals with respect to FBM.In this paper,we define stochastic integrals with respect to FBM as a generalized Stieltjes integral.We give the existence and uniqueness theorems respectively for SDEs driven by fractional Brown motion and their coefficients are local linear growth.

关 键 词：随机微分方程(SDE) 分数Brown运动 广义Stieltjes积分 局部线性增长 适应解 

分 类 号：O211.63[理学—概率论与数理统计]