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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (3): 309-321.doi: 10.3969/j.issn.1005-3085.2019.03.007

• • 上一篇    下一篇

Hilbert空间中由Rosenblatt过程驱动的带有限延迟的随机发展方程

桑利恒1,   吕文华1,   唐  正2   

  1. 1- 滁州学院数学与金融学院，安徽  滁州  239000 
    2- 安徽师范大学数学与统计学院，安徽  芜湖  241000
  • 收稿日期:2017-04-26 接受日期:2018-01-15 出版日期:2019-06-15 发布日期:2019-08-15
  • 基金资助:
    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).

Stochastic Evolution Equations Driven by Rosenblatt Process in a Hilbert Space with Finite Delay

SANG Li-heng1,   LV Wen-hua1,   TANG Zheng2   

  1. 1- School of Mathematics and Finance, Chuzhou University, Chuzhou, Anhui 239000
    2- School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241000
  • Received:2017-04-26 Accepted:2018-01-15 Online:2019-06-15 Published:2019-08-15
  • Supported by:
    The National Natural Science Foundation of China (11271020); the Natural Science Foundation of Anhui Province (1508085QA14); the Distinguished Young Scholars Foundation of Anhui Province (1608085J06); the Natural Science Foundation of Universities in Anhui Province (KJ2016A527; KJ2017A426; KJ2018A0429); the Natural Science Foundation of Chuzhou University (2016QD13).

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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．

关键词: 随机发展方程, 发展算子, Rosenblatt过程, 不动点定理, 适度解

Abstract: 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.

Key words: stochastic evolution equation, evolution operator, Rosenblatt process, fixed point theorem, mild solution

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