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On Probability Measures in Functional Spaces Corresponding to Stationary Gaussian Processes

1964; Society for Industrial and Applied Mathematics; Volume: 9; Issue: 3 Linguagem: Inglês

10.1137/1109057

1095-7219

Yu. A. Rozanov,

Fixed Point Theorems Analysis

Previous article Next article On Probability Measures in Functional Spaces Corresponding to Stationary Gaussian ProcessesYu. A. RozanovYu. A. Rozanovhttps://doi.org/10.1137/1109057PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper is a review (containing also many new results) dealing with the equivalence and perpendicularity of Gaussian measures in functional spaces.[1] Yaroslav Gaek, On a property of normal distribution of any stochastic process, Czechoslovak Math. J., 8 (83) (1958), 610–618, (In Russian.) MR0104290 Google Scholar[2A] Jacob Feldman, Equivalence and perpendicularity of Gaussian processes, Pacific J. Math., 8 (1958), 699–708 MR0102760 0084.13001 CrossrefGoogle Scholar[2B] J. Feldman, Correction to “Equivalence and perpendicularity of Gaussian processes”, Pacific J. Math., 9 (1959), 1295–1296 MR0108852 0089.13502 CrossrefGoogle Scholar[3] Jacob Feldman, Some classes of equivalent Gaussian processes on an interval, Pacific J. Math., 10 (1960), 1211–1220 MR0133864 0097.33802 CrossrefGoogle Scholar[4] Yu. A. Rozanov, On the density of one Gaussian measure with respect to another, Theory Prob. Applications, 7 (1962), 82–87, (English translation.) 10.1137/1107006 0114.34102 LinkGoogle Scholar[5] Yu. A. Rozanov, On the problem of the equivalence of probability measures corresponding to stationary Gaussian processes, Theory of Prob. Applications, 8 (1963), 223–231, (English translation.) 10.1137/1108027 0126.13703 LinkGoogle Scholar[6] I. M. Gel'fand and , A. M. Yaglom, Computation of the amount of information about a stochastic function contained in another such function, Uspehi Mat. Nauk (N.S.), 12 (1957), 3–52, (In Russian.) MR0085153 Google Scholar[7] Emanuel Parzen, Regression analysis of continuous parameter time seriesProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, Univ. California Press, Berkeley, Calif., 1961, 469–489 MR0146931 0107.13802 Google Scholar[8] Jaroslav Hájek, On linear statistical problems in stochastic processes, Czechoslovak Math. J., 12 (87) (1962), 404–444, (In English.) MR0152090 0114.34504 Google Scholar[9] V. F. Pisarenko and , Yu. A. Rozanov, On some problems concerning stationary processes leading to equations related to the Wiener-Hopt equation, Problems of Information Transmission, 14 (1963), 113–135, (In Russian.) Google Scholar[10] M. S. Pinsker, Information and information stability of random variables and processes, Translated and edited by Amiel Feinstein, Holden-Day Inc., San Francisco, Calif., 1964xii+243 MR0213190 0125.09202 Google Scholar[11] D. Slepian, Some comments on the detection of Gaussian signals in Gaussian noise, Trans. IRE, IT-4 (1958), 65–68 10.1109/TIT.1958.1057443 MR0118586 0112.09201 CrossrefGoogle Scholar[12] V. F. Pisarenko, To the problem of detection of a signal on background noise, Radiotekhnika: Elektronika, 6 (1961), 514–528, (In Russian.) Google Scholar[13] V. G. Alekseev, Orthogonality and equivalence conditions for Gaussian measures in a functional space, Dokl. Akad. Nauk SSSR, 147 (1962), 751–754, (In Russian.) MR0146879 Google Scholar[14] Glen Baxter, A strong limit theorem for Gaussian processes, Proc. Amer. Math. Soc., 7 (1956), 522–527 MR0090920 0070.36304 CrossrefGoogle Scholar[15] E. G. Gladyshev, A new limit theorem for stochastic processes with Gaussian increments, Theory Prob. Applications, 6 (1961), 52–61, (English translation.) 10.1137/1106004 0107.12601 LinkGoogle Scholar[16] V. G. Alekseev, On conditions for the perpendicularity of Gaussian measures corresponding to two stochastic processes, Theory Prob. Applications, 8 (1963), 286–290, (English translation.) 10.1137/1108032 0119.34305 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Equivalence of Gaussian measures of multivariate random fields8 August 2014 | Stochastic Environmental Research and Risk Assessment, Vol. 29, No. 2 Cross Ref Absolute Continuity between a Gibbs Measure and Its TranslateE. Nowak25 July 2006 | Theory of Probability & Its Applications, Vol. 49, No. 4AbstractPDF (185 KB)Signal detection in fractional Gaussian noiseIEEE Transactions on Information Theory, Vol. 34, No. 5 Cross Ref On Absolute Continuity of Measures Corresponding to Homogeneous Gaussian FieldsA. V. Skorokhod and M. I. Yadrenko28 July 2006 | Theory of Probability & Its Applications, Vol. 18, No. 1AbstractPDF (1034 KB)On the Estimation of Parameters of a Gaussian Random ProcessV. G. 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