摘要
Rosenblatt过程作为一个重要的自相似随机过程,常被用来刻画非高斯随机现象.为进一步研究Rosenblatt过程对随机现象的刻画,本文考虑由Rosenblatt过程驱动的带有限延迟的一类时间相依随机发展方程适度解的问题.在实值可分Hilbert空间中,运用Banach不动点定理得到了Rosenblatt过程驱动的带有限延迟的随机发展方程适应解的存在性和唯一性,并通过例子说明所得结果是有效的.
As an important self-similar stochastic process, Rosenblatt process is often used to describe non-Gaussian random phenomena. In order to further characterize stochastic phenomena driven by Rosenblatt process, we study the mild solution for a class of time-dependent stochastic evolution equations with finite delay driven by Rosenblatt process in this paper. An existence and uniqueness theorem for the mild solution to this class of stochastic evolution equations is obtained by means of the Banach fixed point theorem in a real separable Hilbert space with time-dependent, and an example is proposed to illustrate the result.
作者
桑利恒
吕文华
唐正
SANG Li-heng;LV Wen-hua;TANG Zheng(School of Mathematics and Finance,Chuzhou University,Chuzhou,Anhui 239000;School of Mathematics and Statistics,Anhui Normal University,Wuhu,Anhui 241000)
出处
《工程数学学报》
CSCD
北大核心
2019年第3期309-321,共13页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(11271020)
安徽省自然科学基金(1508085QA14)
安徽省杰出青年科学基金(1608085J06)
安徽省高校自然科学基金(KJ2016A527
KJ2017A426
KJ2018A0429)
滁州学院自然科学基金(2016QD13)~~
作者简介
桑利恒(1983年8月生),男,博士,讲师.研究方向:随机分析及其应用.
