Conditions for the Equivalence of Distributions of Homogeneous Gaussian Fields

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Previous article Next article Conditions for the Equivalence of Distributions of Homogeneous Gaussian FieldsS. M. KrasnitskiiS. M. Krasnitskiihttps://doi.org/10.1137/1134092PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Feldman, Equivalence and perpendicularity of Gaussian processes, Pacif. J. Math., 8 (1958), 698–708, 9 (1959), pp. 1295–1296 CrossrefGoogle Scholar[2] Yu. A. Rozanov, Infinite-dimensional Gaussian distributions, Trudy Mat. Inst. Steklov., 108 (1968), 136 pp. (errata insert), (In Russian.) 45:7801 Google Scholar[3] A. M. Yaglom, Some classes of random fields in n-dimensional space related to stationary random processes, Theory Probab. Appl.,, 2 (1957), 273–320 LinkGoogle Scholar[4] I. M. Gel'fand and , N. Ya. Vilenkin, Generalized Functions, Vol. 1, Academic Press, New York, 1964 Google Scholar[5] I. A. Ibragimov and , Yu. A. Rozanov, Gaussian random processes, Applications of Mathematics, Vol. 9, Springer-Verlag, New York, 1978x+275, New York 80f:60038 CrossrefGoogle Scholar[6] Z. S. Zerakidze, On the equivalence of distributions of homogeneous fields, Trudy in-ta prikladnoi matematiki Tbilisskogo universiteta, 2 (1969), 215–220, (In Russian.) Google Scholar[7] A. V. Skorokhod and , M. I. Yadrenko, On absolute continuity of measures corresponding to homogeneous random fields, Theory Probab. Appl., 18 (1973), 27–40 10.1137/1118002 0282.60026 LinkGoogle Scholar[8] S. M. Krasnitskii, On conditions of equivalence and perpendicularity of measures corresponding to homogeneous Gaussian fields, Theory Probab. Appl., 18 (1973), 588–592 10.1137/1118075 0334.60021 LinkGoogle Scholar[9] V. S. Vladimirov, Generalized Functions in Mathematical Physics, Nauka, Moscow, 1976, (In Russian.) Google Scholar[10] I. M. Gel'fand and , G. E. Shilov, Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian P. Peltzer, Academic Press, New York, 1968x+261, London 37:5693 Google Scholar[11] S. Bochner and , W. Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948ix+216 10,366a Google Scholar[12] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969xiv+676 41:1976 Google Scholar[13] S. M. Nikol'skii, Approximation of functions of several variables and imbedding theorems, Springer-Verlag, New York, 1975viii+418 51:11073 CrossrefGoogle Scholar[14] L. Hormander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Bd. 116, Academic Press Inc., Publishers, New York, 1963vii+287 28:4221 CrossrefGoogle Scholar[15] S. M. Krasnitskii, On conditions of equivalence of distributions of homogeneous Gaussian fields, Summaries of Reports of the 4th International Vilna conference on Probability Theory and Mathematical Statistics, Vol. 2, Institute of Math. and Cybern. of the Lithuanian Acad. Sci., 1985, 72–74, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spacesThe Annals of Statistics, Vol. 50, No. 2 Cross Ref Volume 34, Issue 4| 1990Theory of Probability & Its Applications History Submitted:30 July 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1134092Article page range:pp. 720-725ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics