带分数Brown运动和局部线性增长的随机微分方程

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 200-211.

带分数Brown运动和局部线性增长的随机微分方程

冉启康()

^{上海财经大学数学学院上海 200433}

收稿日期:2017-08-30 出版日期:2020-02-26 发布日期:2020-04-08
作者简介:冉启康, E-mail:ranqikang@mail.shufe.edu.cn
基金资助:
国家自然科学基金(11601306)

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

Qikang Ran()

^{College of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433}

Received:2017-08-30 Online:2020-02-26 Published:2020-04-08
Supported by:
国家自然科学基金(11601306)

摘要/Abstract

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 ∈（$\frac{1}{2}$，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.

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

Abstract:

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 ∈ ($\frac{1}{2}$, 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.

Key words: Stochastic differential equations(SDE), Fractional Brownian motion, Generalized Stieltjes integral, Local linear growth, Adapted solution

中图分类号:

O211.63

冉启康. 带分数Brown运动和局部线性增长的随机微分方程[J]. 数学物理学报, 2020, 40(1): 200-211.

Qikang Ran. SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth[J]. Acta mathematica scientia,Series A, 2020, 40(1): 200-211.

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