Abstract
Paper No. 27 has by now become classical and opened the main road in the theory of stationary (and related) random processes, giving a proper setting1 for prediction problems and solving them for stationary processes with discrete time (stationary sequences). This work is remarkable because of its deep connection with various questions of approximation theory, spectral theory of operators in Hubert space and the theory of analytic functions. The two central notions in this theory are the regularity of a random process and subordination of one process to another.
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References
Yu.A. Rozanov, Stationary random processes, Fizmatgiz, Moscow, 1963 (in Russian).
C. Goffman, Banach spaces of analytic functions, Prentice-Hall, 1962.
B. Szökefalvi-Nagy and Ch. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, 1970 (translation from the French).
Yu.A. Rozanov, Theory of renewal processes, Nauka, Moscow, 1974 (in Russian).
H. Dym and H.P. McKean, Gaussian processes, function theory and inverse spectral problems, Academic Press, New York, 1976.
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© 1992 Springer Science+Business Media Dordrecht
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Rozanov, Y.A. (1992). Stationary Sequences (No. 27). In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_60
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DOI: https://doi.org/10.1007/978-94-011-2260-3_60
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5003-6
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