Geodesic
On stationary stochastic processes with fuzzy states
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 91-108

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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.
Keywords: continuous random processes with fuzzy states, fuzzy expectations, covariance functions, stationary fuzzy-random processes, ergodicity property
Mots-clés : spectral decomposition 
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     title = {On stationary stochastic processes with fuzzy states},
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V. L. Khatskevich. On stationary stochastic processes with fuzzy states. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 1, pp. 91-108. http://geodesic.mathdoc.fr/item/VUU_2024_34_1_a6/