由分数布朗运动驱动的随机泛函微分方程(0

Existence and uniqueness of solutions to stochastic functional differential equations(0 我的收藏 名 称： 注 释：

作　　者：郭兰兰 丁小丽 高宇 GUO Lanlan;DING Xiaoli;GAO Yu(School of Science,Xi’an Polytechnic University,Xi’an 710600,China)

机构地区：[1]西安工程大学理学院,西安710600

出　　处：《延边大学学报(自然科学版)》2024年第4期1-7,共7页Journal of Yanbian University(Natural Science Edition)

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：利用Picard迭代法讨论了由分数布朗运动驱动的随机泛函微分方程:{dX(t)=(AX(t))+f(t,X_(t))dt+g(t)dB^(H)(t),t∈[0,T]X(t)=ζ(t),t∈[-r,0],r≥0,解的存在唯一性,其中Hurst指数为0<H<1/2.首先,通过对此类方程的分数布朗运动的积分进行估计,得到了其随机积分的矩不等式;其次,利用解析半群定义了此类方程的温和解;最后,在相关假设条件下利用Picard迭代法构造了此类方程的迭代序列,并证明了此类方程的温和解是存在且唯一的.The existence and uniqueness of solutions for stochastic functional differential equations driven by fractional Brownian motion:{dX(t)=(AX(t))+f(t,X_(t))dt+g(t)dB^(H)(t),t∈[0,T]X(t)=ζ(t),t∈[-r,0],r≥0,are discussed by using Picard iterative method,where Hurst index is 0<H<1/2.Firstly,by estimating the integral of the fractional Brownian motion of the equation,the moment inequality of the random integral is obtained.Secondly,the mild solution of this kind of equation is defined by using analytic semigroup.Finally,under the relevant assumptions,the iterative sequence is constructed by using the iterative method,and it is proved that the mild solution of this kind of equation exists and is unique.

关 键 词：随机泛函微分方程 分数布朗运动 Picard迭代法 HURST指数 矩估计不等式 

分 类 号：O175.1[理学—数学]