On stationary random processes with fuzzy states

被引：0

作者：

Khatskevich, V. L. ^{[1
,2
]}

机构：

[1] Air Force Acad, Dept Math, Engn, Ul Old Bolsheviks 54a, Voronezh 394052, Russia

[2] Air Force Acad, Dept Math, Ul Old Bolsheviks 54a, Voronezh 394052, Russia

来源：

VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI | 2024年 / 34卷 / 01期

关键词：

continuous random processes with fuzzy states; fuzzy expectations; covariance functions; stationary fuzzy-random processes; ergodicity property; spectral decomposition; VARIANCE;

D O I：

10.35634/vm240107

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, continuous random processes with fuzzy states are studied. The properties of their numerical characteristics - fuzzy expectations, expected values and covariance functions - are established. The main attention is paid to the class of stationary fuzzy -random processes. For them, the ergodicity property and the spectral representation of covariance function (generalized Wiener-Khinchin theorem) are substantiated. The results obtained are based on the properties of fuzzy -random variables and numerical random processes. Triangular fuzzy -random processes are considered as examples.

引用

页码：91 / 108

页数：18

共 33 条

[1]

Ahmad L, 2014, Arxiv, DOI arXiv:1403.0242

[2] INTEGRALS OF SET-VALUED FUNCTIONS [J].