具有分数Brown运动的分数阶中立型随机微分方程解的存在唯一性  

Existence and uniqueness of solutions to fractional neutral stochastic differential equations with fractional brownian motion

作　　者：李国平[1] 韩婷[1,2] Li Guoping;Han Ting(Xinhua College,Ningxia University,Yinchuan 750021,China;College of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学新华学院,银川750021 [2]宁夏大学数学统计学院,银川750021

出　　处：《河南师范大学学报(自然科学版)》2025年第3期104-111,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：宁夏高等学校科学研究项目(NYG2024219;NYG2022114);国家自然科学基金(62063028).

摘　　要：研究了一类在Hilbert空间中具有分数Brown运动的分数阶中立型随机微分方程,利用Picard逐步逼近法得到了其非Lipschitz条件和弱化的线性增长条件下粘性解的新的存在唯一性的充分条件.所提的研究方法使得先前一些研究结果得到了拓展.最后通过具有分数Brown运动的随机非线性波动方程验证了理论的有效性.In this paper,we consider a class of fractional-order neutral stochastic differential equations with fractional Brownian motion by using picard step by step in a Hilbert space.A novel sufficient condition for the existence and uniqueness of mild solutions is obtained in conditions of the non-Lipschitz condition and the weakened linear growth.The result generalizes a few previous known results.An application to the stochastic nonlinear wave equation with fractional Brownian motion is given to illustrate the validity of the obtained theory.

关 键 词：分数阶随机微分方程 分数Brown运动 粘性解 存在唯一性 

分 类 号：O175.14[理学—数学]