On the Canonical Hida-Craméer Representation for Random Processes
Z. A. Ivkovich, Yu. A. Rozanov · Theory of Probability and Its Applications · 1971
Previous article Next article On the Canonical Hida-Craméer Representation for Random ProcessesZ. Ivkovich and Yu. A. RozanovZ. Ivkovich and Yu. A. Rozanovhttps://doi.org/10.1137/1116033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Herman Wold, A study in the analysis of stationary time series, Almqvist and Wiksell, Stockholm, 1954viii+236, 2nd Ed. MR0061344 0055.13401 Google Scholar[2] H. Cramér, Stochastic processes as curves in Hilbert space, Theory Prob. Applications, 9 (1964), 169–179 0161.14602 LinkGoogle Scholar[3] Takeyuki Hida, Canonical representations of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math., 33 (1960/1961), 109–155 MR0119246 0100.34302 CrossrefGoogle Scholar[4] Yu. A. Rozanov, Stationary random processes, Translated from the Russian by A. Feinstein, Holden-Day Inc., San Francisco, Calif., 1967vi+211 MR0214134 0152.16302 Google Scholar[5] G. Kallianpur and , U. Mandrekar, Multiplicity and representation theory of purely non-deterministic stochastic processes, Theory Prob. Applications, 10 (1965), 553–581 10.1137/1110073 0171.38902 LinkGoogle Scholar[6] Kari Karhunen, Über lineare Methoden in der Wahrscheinlichkeitsrechnung, Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys., 1947 (1947), 79– MR0023013 0030.16502 Google Scholar[7] V. Mandrekar, On multivariate wide-sense Markov processes, Nagoya Math. J., 33 (1968), 7–19 MR0248909 0174.49602 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Transformation of a Continuous Gaussian Process by Rarefying Its Innovation ProcessTheory of Probability & Its Applications, Vol. 33, No. 4 | 28 July 2006AbstractPDF (476 KB)On the Rank of the Projection of a Random ProcessTheory of Probability & Its Applications, Vol. 20, No. 2 | 17 July 2006AbstractPDF (277 KB)Information Sciences, Vol. 10, No. 1 | 1976 Cross Ref Linear Innovation TheoremsInformation Sciences, Vol. 10, No. 2 | 1 Jan 1976 Cross Ref On Canonical Representations for Stochastic Processes of Multiplicities One and TwoTheory of Probability & Its Applications, Vol. 18, No. 1 | 28 July 2006AbstractPDF (508 KB)Innovation and Nonanticipative ProcessesMultivariate Analysis–III | 1 Jan 1973 Cross Ref Volume 16, Issue 2| 1971Theory of Probability & Its Applications199-399 History Submitted:30 October 1970Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1116033Article page range:pp. 351-356ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics