On Strong Convergence of Distributions of Functionals of Random Processes. I

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Previous article Next article On Strong Convergence of Distributions of Functionals of Random Processes. IYu. A. DavydovYu. A. Davydovhttps://doi.org/10.1137/1125091PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Appl., 1 (1956), 157–214 LinkGoogle Scholar[2] V. A. Rokhlin, On the functional concepts of measure theory, Matem. Sb., 25, 25 (67) (1949), 107–150, (In Russian.) Google Scholar[3] Jacques Neveu, Mathematical foundations of the calculus of probability, Translated by Amiel Feinstein, Holden-Day Inc., San Francisco, Calif., 1965xiii+223 33:6660 0137.11301 Google Scholar[4] A. V. Skorokhod, Integration in Hilbert space, Springer-Verlag, New York, 1974xii+177 57:6360 CrossrefGoogle Scholar[5] I. I. Gikhman and , A. V. Skorokhod, Introduction to the theory of random processes, Translated from the Russian by Scripta Technica, Inc, W. B. Saunders Co., Philadelphia, Pa., 1969xiii+516 40:923 Google Scholar[6] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[7] D. Geman and , J. Horowitz, Occupation times for smooth stationary processes, Ann. Probability, 1 (1973), 131–137 50:3325 0264.60027 CrossrefGoogle Scholar[8] R. H. Cameron and , W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2), 45 (1944), 386–396 6,5f 0063.00696 CrossrefGoogle Scholar[9] Yu. A. Rozanov, Infinite-dimensional Gaussian distributions, Trudy Mat. Inst. Steklov., 108 (1968), 136 pp. (errata insert), (In Russian.) 45:7801 Google Scholar[10] I. S. Borisov, Masters Thesis, An Investigation of the Rate of Convergence in the Invariance Principle, candidate's thesis, Novosibirsk, 1978, (In Russian.) Google Scholar[11] P. Billingsley and , F. Topsoe, Uniformity in weak convergence, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 7 (1967), 1–16 35:326 0147.15701 CrossrefGoogle Scholar[12] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar[13] I. A. Ibragimov and , R. Z. Khas'minskh, Asymptotic behavior of some statistical estimators, I, II, Theory Prob. Appl., 17 (1972), 445–462, 18 (1973), pp. 76–91 LinkGoogle Scholar[14] A. M. Kagan, , Yu. V. Linnik and , S. R. Rao, Characterization problems in mathematical statistics, John Wiley & Sons, New York-London-Sydney, 1973xii+499 49:11689 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema6 February 2019 | Vestnik St. Petersburg University, Mathematics, Vol. 51, No. 4 Cross Ref Local Limit Theorems for Functionals of Random ProcessesYu. A. Davydov28 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 4AbstractPDF (692 KB)An Application of the Stratification Method to the Study of Functionals of Processes with Independent IncrementsM. A. Lifshits17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 4AbstractPDF (1060 KB)Summary of Reports Presented at Sessions of the Probability and Mathematical Statistics Seminar at the Leningrad Section of the Mathematical Institute of the USSR Academy of Sciences, 198228 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 4AbstractPDF (1219 KB)On the Absolute Continuity of Distributions of Functionals of Random ProcessesM. A. Lifshits17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 3AbstractPDF (756 KB)The Fiber Method and Its Application to the Study of Functionals of Stochastic ProcessesM. A. Lifshits17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 1AbstractPDF (1262 KB)Summary of Reports Presented at Sessions of the Probability and Mathematical Statistics Seminar at the Leningrad Section of the Mathematical Institute of the USSR Academy of Sciences, 198017 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 4AbstractPDF (605 KB) Volume 25, Issue 4| 1981Theory of Probability & Its Applications History Submitted:25 December 1978Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1125091Article page range:pp. 772-789ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics