Geodesic
On some properties of stationary stochastic processes with fuzzy states
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 118-126

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In this work, continuous stochastic processes with fuzzy states are studied. The main attention is paid to the class of stationary fuzzy stochastic processes. The properties of their numerical characteristics are established: fuzzy expectations, expectations, and correlation functions. Their spectral representation and the generalized Wiener–Khinchin theorem are substantiated. The results obtained are based on the properties of fuzzy stochastic variables and numerical stochastic processes. Triangular fuzzy stochastic processes are considered as examples.
Keywords: continuous stochastic process, fuzzy state, fuzzy expectation, correlation function
Mots-clés : spectral decomposition 
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     author = {V. L. Khatskevich},
     title = {On some properties of stationary stochastic processes with fuzzy states},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {118--126},
     publisher = {mathdoc},
     volume = {233},
     year = {2024},
     language = {ru},
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V. L. Khatskevich. On some properties of stationary stochastic processes with fuzzy states. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 118-126. http://geodesic.mathdoc.fr/item/INTO_2024_233_a10/