Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian Process

Previous article Next article Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian ProcessT. L. MalevichT. L. Malevichhttps://doi.org/10.1137/1114035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 E. V. Bulinskaya, On the mean number of crossings of a level by a stationary Gaussian process, Theory Prob. Applications, 6 (1961), 435–438 10.1137/1106059 0108.31002 LinkGoogle Scholar2 V. A. Ivanov, On the mean number of crossings of a level by sample functions of a stochastic process, Theory Prob. Applications, 5 (1960), 319–323 10.1137/1105031 0100.34101 LinkGoogle Scholar3 G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc., 71 (1951), 38–69 MR0051340 0043.30601 CrossrefGoogle Scholar4 Harald Cramér and , M. R. Leadbetter, The moments of the number of crossings of a level by a stationary normal process, Ann. Math. Statist., 36 (1965), 1656–1663 MR0185682 0137.35603 CrossrefGoogle Scholar5A S. O. 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Applications, 10 (1965), 457–465 10.1137/1110053 0161.15702 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The sharp phase transition for level set percolation of smooth planar Gaussian fieldsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 56, No. 2 | 1 May 2020 Cross Ref The winding of stationary Gaussian processesProbability Theory and Related Fields, Vol. 172, No. 1-2 | 24 November 2017 Cross Ref Critical points of multidimensional random Fourier series: Central limitsBernoulli, Vol. 24, No. 2 | 1 May 2018 Cross Ref Periodicity in the autocorrelation function as a mechanism for regularly occurring zero crossings or extreme values of a Gaussian processPhysical Review E, Vol. 96, No. 6 | 18 December 2017 Cross Ref A CLT concerning critical points of random functions on a Euclidean spaceStochastic Processes and their Applications, Vol. 127, No. 10 | 1 Oct 2017 Cross Ref The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian ProcessesVulnerability, Uncertainty, and Risk | 7 July 2014 Cross Ref Limit Theorems for Excursion Sets of Stationary Random FieldsModern Stochastics and Applications | 28 December 2013 Cross Ref Macroscaling Limit Theorems for Filtered Spatiotemporal Random FieldsStochastic Analysis and Applications, Vol. 31, No. 3 | 1 May 2013 Cross Ref ReferencesApplications of Random Process Excursion Analysis | 1 Jan 2013 Cross Ref Sample Functions of the Gaussian ProcessSelected Works of R.M. 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I. PiterbargTheory of Probability & Its Applications, Vol. 23, No. 1 | 17 July 2006AbstractPDF (374 KB)A Limit Theorem for the Length of Contours Generated by Crossings of the Zero Level by Gaussian FieldsT. L. MalevicTheory of Probability & Its Applications, Vol. 19, No. 3 | 28 July 2006AbstractPDF (811 KB)Level-crossing problems for random processesIEEE Transactions on Information Theory, Vol. 19, No. 3 | 1 May 1973 Cross Ref Volume 14, Issue 2| 1969Theory of Probability & Its Applications183-371 History Submitted:05 September 1967Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1114035Article page range:pp. 287-295ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics