Existence and uniqueness for solutions of mixed stochastic delay differential equations

被引：0
作者：
Weiguo Liu
Qianyi Yu
Xinwen Zhang
机构：
[1] Guangdong University of Finance and Economics,School of Statistics and Mathematics
[2] Guangzhou College of Commerce,School of Information Technology and Engineering
来源：
Research in the Mathematical Sciences | 2021年 / 8卷
关键词：
Stochastic delay differential equation; Existence and uniqueness; Brownian motion; Fractional Brownian motion; 41A25; 60G22; 60H10;
D O I：
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摘要：
We consider a class of one-dimensional mixed stochastic delay differential equations driven by Brownian motions and fractional Brownian motions with Hurst parameter H∈(12,1).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H\in (\frac{1}{2},1).$$\end{document} A existence and uniqueness result is proved by using a contraction principle and some priori estimations. Some previous works are generalized and improved partially.
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