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

1968; Society for Industrial and Applied Mathematics; Volume: 13; Issue: 2 Linguagem: Inglês

10.1137/1113036

1095-7219

Yu. K. Belyaev,

Advanced Statistical Methods and Models

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 SectionsAbout[1] S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J., 24 (1945), 46–156 MR0011918 (6,233i) 0063.06487 CrossrefGoogle Scholar[2] 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 Scholar[3] 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 Scholar[4] B. V. Gnedenko, , Yu. K. Belyaev and , A. D. Solov'ev, Mathematical Methods in Reliability Theory, Izd-vo "Nauka", Mokvsa, 1965, (In Russian.) Google Scholar[5] 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 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 MR0217860 (36:949) 0162.21102 Google Scholar[7] Yu. K. Belyaev, Bursts and shines of random fields, Soviet Math. 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