Section
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Mathematics
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Title
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On stationary random processes with fuzzy states
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Author(-s)
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Khatskevich V.L.a
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Affiliations
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Air Force Academy named after Professor N. E. Zhukovsky and Yu.A. Gagarina
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Abstract
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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.
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Keywords
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continuous random processes with fuzzy states, fuzzy expectations, covariance functions, stationary fuzzy-random processes, ergodicity property, spectral decomposition
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UDC
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519.218.84
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MSC
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60G10
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DOI
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10.35634/vm240107
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Received
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3 June 2023
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Language
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Russian
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Citation
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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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References
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