Previous |  Up |  Next


The author in the paper evaluates the Rényi distances between two Gaussian measures using properties of nuclear operators and expresses the formula for the asymptotic rate of the Rényi distances of stationary Gaussian measures by the corresponding spectral density functions in a general case.
[1] Gohberg I., Krein M.: An Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space. Nauka, Moscow 1965. In Russian MR 0220070
[2] Grenander V.: A contribution to the theory of Toeplitz matrices. Trans. Amer. Math. Soc. 79 (1955), 124–140 DOI 10.1090/S0002-9947-1955-0070044-8 | MR 0070044 | Zbl 0065.35302
[3] Grenander V., Szegő G.: Toeplitz Forms and their Application. Innostrannaja literatura, Moscow 1961. In Russian MR 0130488
[4] Hájek J.: On linear statistical problems. Czechoslovak Math. J. 12 (87) (1962), 3, 404–444 MR 0152090 | Zbl 0114.34504
[5] Kac M.: Toeplitz matrices, translation kernels and related problems in probability theory. Duke Math. J. 21 (1954), 501–509 MR 0062867
[6] Kadota T.: Simultaneous diagonalization of two covariance kernels and application to second order stochastic process. SIAM J. Appl. Math. 15 (1967), 1470–1480 DOI 10.1137/0115127 | MR 0241881
[7] Kullback S., Keegel J. C., Kullback J. H.: Topics in Statistical Information Theory (Lecture Notes in Statistics 42). Springer–Verlag, Berlin 1987 MR 0904477
[8] Michálek J.: Asymptotic Rényi’s rate of Gaussian processes. Problem Control Inform. Theory 18 (1990), 8, 209–227 Zbl 0705.62079
[9] Michálek J., Rüschendorf L.: Karhunen class processes forming a basis. In: Trans. 12th Prague Conference on Inform. Theory, Statist. Decis. Functions, Random Process., Prague 1992, Academy of Sciences of the Czech Republic, pp. 158–160
[10] Pinsker M. S.: Information and Information Stability of Random Variables and Processes. Izv. AN SSSR, Moscow 1960. In Russian MR 0191718
[11] Pisarenko B.: On the problem of detection of random signal in noise. Radiotekhn. i Elektron. 6 (1961), 4, 514–528 In Russian MR 0141540
[12] Pitcher T.: An integral expression for the log likelihood ratio of two Gaussian processes. SIAM J. Appl. Math. 14 (1966), 228–233 DOI 10.1137/0114020 | MR 0211499 | Zbl 0142.13902
[13] Rozanov J.: Infinite–Dimensional Gaussian Probability Distributions. Nauka, Moscow 1968. In Russian
[14] Vajda I.: Theory of Statistical Inference and Information. Kluwer, Dordrecht 1989 Zbl 0711.62002
Partner of
EuDML logo