分数布朗运动驱动的随机微分方程的稳定性  

Stability of the stochastic differential equation driven by fractional Brownian motion

作　　者：高宇 丁小丽 郭兰兰 GAO Yu;DING Xiaoli;GUO Lanlan(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《黑龙江大学自然科学学报》2024年第2期163-169,共7页Journal of Natural Science of Heilongjiang University

基　　金：陕西省科技厅自然科学基础研究计划项目(2023-JC-YB-030)。

摘　　要：考虑如下形式的由分数布朗运动驱动的随机微分方程的均方指数稳定性,{dX(t)=(AX(t)+f(t,X(t))dt+g(t)dB^(H)(t)X(t)=φ(t),t∈[0,T]式中Hurst参数H∈(0,1/2)。通过对该方程中分数布朗运动的维纳积分进行估计,得到矩估计不等式。在一些特定条件下,采用积分不等式讨论了温和解的稳定性,给出相应的例子,验证了结论的准确性。The mean square exponential stability of the stochastic differential equations driven by fractional Brownian motion of the following form is considered,{dX(t)=(AX(t)+f(t,X(t))dt+g(t)dB^(H)(t)X(t)=φ(t),t∈[0,T]where H∈(0,1/2).The moment estimation inequality is obtained by estimating the Wiener integral of the fractional Brownian motion in this equation.The stability of the mild solution is discussed by utilizing the integral inequality under some specific conditions.Corresponding examples are given to verify the accuracy of the conclusions.

关 键 词：随机微分方程 分数布朗运动 温和解 均方指数稳定性 积分不等式 

分 类 号：O175.1[理学—数学]