模糊随机过程的Itô-Henstock积分

doi:10.6040/j.issn.1671-9352.0.2019.235

摘要/Abstract

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

巩增泰, 宿爱. 模糊随机过程的Itô-Henstock积分[J]. 《山东大学学报(理学版)》, 2019, 54(8): 1-13.

GONG Zeng-tai, SU Ai. Itô-Henstock integration of the fuzzy stochastic process[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 1-13.

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