The Local Structure of a Homogeneous Gaussian Random Field in a Neighborhood of High Level Points

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Previous article Next article The Local Structure of a Homogeneous Gaussian Random Field in a Neighborhood of High Level PointsV. P. NoskoV. P. Noskohttps://doi.org/10.1137/1130096PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. P. Nosko, Local structure of Gaussian random fields in the neighborhood of high-level shines, Dokl. Akad. Nauk SSSR, 189 (1969), 714–717, (In Russian.) 41:4640 Google Scholar[2] V. P. Nosko, Characteristics of ejections of Gaussian homogeneous fields over a high level, Proc. Nippo-Soviet Symposium on Probability Theory, Khabarovsk, August 1969, Izd-vo SO AN SSR, Novosibirsk, 1969, 209–215, (In Russian.) Google Scholar[3] Yu. K. Belyaev, H. Cramér and , M. Leadbetter, New results and generalizations of crossing type problemsRandom Processes, Mir, Moscow, 1969, 341–378, Supplement, (In Russian.) Google Scholar[4] Yu. K. Belyaev, Random point sets and problems of level crossing typeEjections of Random Fields, MGU, Moscow, 1972, (In Russian.) Google Scholar[5] Yu. K. Belyayev, Point processes and first passage problems, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, Univ. California Press, Berkeley, Calif., 1972, 1–17 53:4207 0279.60037 Google Scholar[6] Harald Cramér and , M. R. Leadbetter, Stationary and related stochastic processes. Sample function properties and their applications, John Wiley & Sons Inc., New York, 1967xii+348 36:949 0162.21102 Google Scholar[7] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 15,445b 0053.26802 Google Scholar[8] Yu. K. Belyaev, General formula for the mean number of crossings for random processes and fieldsEjections of Random Fields, MGU, Moscow, 1972, 38–45, (In Russian.) Google Scholar[9] T. L. Malevich, The formula for the mean number of crossings of a surface by random fields, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk, 17 (1973), 15–17, 75, (In Russian.) 49:8095 Google Scholar[10] Robert J. Adler, The geometry of random fields, John Wiley & Sons Ltd., Chichester, 1981xi+280 82h:60103 0478.60059 Google Scholar[11] T. W. Anderson, An introduction to multivariate statistical analysis, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1984xviii+675 86b:62079 0651.62041 Google Scholar[12] R. M. Dudley, Gaussian processes on several parameters, Ann. Math. Statist., 36 (1965), 771–788 33:796 0142.14001 CrossrefGoogle Scholar[13] V. P. Nosko, Masters Thesis, Investigation of ejections of random processes and fields, Dissertation for Candidate's Degree, MGU, Moscow, 1970, (In Russian.) Google Scholar[14] Richard J. Wilson and , Robert J. Adler, The structure of Gaussian fields near a level crossing, Adv. in Appl. Probab., 14 (1982), 543–565 84c:60061 0487.60044 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On shape of high massive excursions of trajectories of Gaussian homogeneous fields24 December 2016 | Extremes, Vol. 20, No. 3 Cross Ref On the Shape of Trajectories of Gaussian Processes Having Large Massive ExcursionsE. V. Kremena, V. I. Piterbarg, and J. Hüsler19 December 2014 | Theory of Probability & Its Applications, Vol. 58, No. 4AbstractPDF (244 KB)References and Suggested Reading21 July 2008 Cross Ref The Investigation of High-Level Excursions of Gaussian Fields: A Fresh Approach Involving ConvexityV. P. Nosko17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 1AbstractPDF (711 KB)Mathematical Reliability-Theoretical Research at the Probability Theory DepartmentYu. K. Belyaev, B. V. Gnedenko, and A. D. Solov’ev17 July 2006 | Theory of Probability & Its Applications, Vol. 34, No. 1AbstractPDF (930 KB)Asymptotic Distributions of Characteristics of High-Level Overshoots of a Homogeneous Gaussian Random FieldV. P. Nosko17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 4AbstractPDF (966 KB)Model fields in crossing theory: a weak convergence perspective1 July 2016 | Advances in Applied Probability, Vol. 20, No. 04 Cross Ref Model fields in crossing theory: a weak convergence perspective1 July 2016 | Advances in Applied Probability, Vol. 20, No. 4 Cross Ref Volume 30, Issue 4| 1986Theory of Probability & Its Applications History Submitted:01 December 1983Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130096Article page range:pp. 767-782ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics