带分布延迟的随机卷积的正则性  

Regularity of stochastic convolution with distributed delay

作　　者：贾倩 王伟 JIA Qian;WANG Wei(School of Mathematical Science,Tianjin Normal University,Tianjin 300387)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《首都师范大学学报(自然科学版)》2025年第2期18-23,共6页Journal of Capital Normal University:Natural Science Edition

基　　金：天津师范大学研究生科研创新项目(2022KYCX114Y);国家自然科学基金项目(11401436)。

摘　　要：本文讨论了一类线性随机泛函微分方程的随机卷积的正则性,这类带分布延迟的随机泛函微分方程是由分数布朗运动驱动的。利用基本解的估计和分数布朗运动的性质得到了随机卷积的正则性。特别地,在方程的系数算子符合一些特定条件时,给出了满足随机卷积的正则性的条件。This paper discusses the regularity of stochastic convolution of a class of linear stochastic functional differential equations with distributed delay driven by fractional Brownian motion.In this paper,the regularity of stochastic convolution is obtained by using the estimation of fundamental solutions and the properties of fractional Brownian motion.In particular,when the coefficient operator of the equation conforms to some specific conditions,this paper gives a condition satisfying the regularity of stochastic convolution.

关 键 词：正则性 分数布朗运动 随机卷积 基本解 

分 类 号：O211.63[理学—概率论与数理统计]