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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (8): 1-13.doi: 10.6040/j.issn.1671-9352.0.2019.235

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模糊随机过程的Itô-Henstock积分

巩增泰,宿爱   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 出版日期:2019-08-20 发布日期:2019-07-03
  • 作者简介:巩增泰(1965— )男, 博士, 教授, 研究方向为模糊分析学和粗糙集理论. Email:zt-gong@163.com
  • 基金资助:
    国家自然科学基金资助项目(61763044)

Itô-Henstock integration of the fuzzy stochastic process

GONG Zeng-tai, SU Ai   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Online:2019-08-20 Published:2019-07-03

摘要: 定义和讨论了适应的模糊随机过程关于Brownian运动的模糊Itô-Henstock积分和模糊Itô-McShane积分及其性质,给出了刻画定理,并讨论了两者之间的相互关系。结果表明,当模糊Itô-Henstock积分原函数Itô 绝对连续时,模糊Itô-Henstock积分和模糊Itô-McShane积分等价。

关键词: 模糊数, 模糊随机变量, Brownian 运动, 模糊随机过程, 模糊 Itô, 积分

Abstract: The fuzzy Itô-Henstock integral and the fuzzy Itô-McShane integrals for adapted fuzzy stochastic process with respect to a Brownian motion are defined and their properties are discussed. In addition, the characterization theorems are given and their interrelation of between the fuzzy Itô-Henstock integral and the fuzzy Itô-McShane integral is investigated. The result shows that the fuzzy Itô-Henstock integral is equivalent to the fuzzy Itô-McShane integral when its primitive of fuzzy Itô-Henstock integral is Itô absolutely continuous.

Key words: fuzzy number, fuzzy stochastic variable, Brownian motion, fuzzy stochastic process, fuzzy Itô, integral

中图分类号: 

  • O172.2
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