On the Number of Exits Across the Boundary of a Region by a Vector Stochastic Process

Previous article Next article On the Number of Exits Across the Boundary of a Region by a Vector Stochastic ProcessYu. K. BelyaevYu. K. Belyaevhttps://doi.org/10.1137/1113036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J., 24 (1945), 46–156 MR0011918 (6,233i) 0063.06487 CrossrefGoogle Scholar2 Yu. K. Belyaev, On the number of intersections of a level by a Gaussian stochastic process, I, Theory Prob. Applications, 11 (1966), 106–113 10.1137/1111006 0161.14703 LinkGoogle Scholar3 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 (32:3144) 0137.35603 CrossrefGoogle Scholar4 B. V. Gnedenko, , Yu. K. Belyaev and , A. D. Solov'ev, Mathematical Methods in Reliability Theory, Izd-vo "Nauka", Mokvsa, 1965, (In Russian.) Google Scholar5 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 Scholar6 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 MR0217860 (36:949) 0162.21102 Google Scholar7 Yu. K. Belyaev, Bursts and shines of random fields, Soviet Math. Dokl., 8 (1967), 1107–1109, (English translation.) 0192.54801 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Long‐term prediction intervals with many covariates28 December 2021 | Journal of Time Series Analysis, Vol. 43, No. 4 Cross Ref Structural and System Reliability13 January 2022 | , Vol. 1 Cross Ref Series System Reliability of Uncertain Linear Structures under Gaussian Excitation by Cross Entropy–Based Importance SamplingJournal of Engineering Mechanics, Vol. 148, No. 1 Cross Ref Zuverlässigkeit von Tragwerken22 June 2022 Cross Ref Layered Stochastic Approximation Monte-Carlo method for tall building and tower fragility in mixed wind load climatesEngineering Structures, Vol. 239 Cross Ref A new approach to estimate the collision probability for automotive applicationsAutomatica, Vol. 127 Cross Ref Analytic Collision Risk Calculation for Autonomous Vehicle Navigation Cross Ref Dynamic Lognormal Shadowing Framework for the Performance 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