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Russia Voronezh
Section Mathematics
Title On stationary random processes with fuzzy states
Author(-s) Khatskevich V.L.a
Affiliations Air Force Academy named after Professor N. E. Zhukovsky and Yu.A. Gagarina
Abstract 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.
Keywords continuous random processes with fuzzy states, fuzzy expectations, covariance functions, stationary fuzzy-random processes, ergodicity property, spectral decomposition
UDC 519.218.84
MSC 60G10
DOI 10.35634/vm240107
Received 3 June 2023
Language Russian
Citation Khatskevich V.L. On stationary random processes with fuzzy states, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 1, pp. 91-108.
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