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Teoriya Veroyatnostei i ee Primeneniya, 1966, Volume 11, Issue 1, Pages 120–128 (Mi tvp571)  
This article is cited in 31 scientific papers (total in 31 papers)

Short Communications

On the number of intersections of a level by a Gaussian stochastic process. I

Yu. K. Belyaevab

a Moscow
b Stockholm
Full-text PDF (541 kB) Citations (31)
Abstract: In this first part we are concerned with the questions connected with moments of high order of the number of intersections for a Gaussian process $\xi_t$ (which is in general nonstationary). It is proved that for factorial moments an explicit and comparatively simple formula (11) can be obtained. If $\xi_t$ has the derivative $\xi_t^{(k)}$ then the moment of order $k$ of the number of intersections is finite. In the second part we shall consider some limit theorems for max $\xi_t$ and for the number of intersections of high level.
Received: 13.05.1965
English version:
Theory of Probability and its Applications, 1966, Volume 11, Issue 1, Pages 106–113
DOI: https://doi.org/10.1137/1111006
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. K. Belyaev, “On the number of intersections of a level by a Gaussian stochastic process. I”, Teor. Veroyatnost. i Primenen., 11:1 (1966), 120–128; Theory Probab. Appl., 11:1 (1966), 106–113
Citation in format AMSBIB
\Bibitem{Bel66}
\by Yu.~K.~Belyaev
\paper On the number of intersections of a~level by a~Gaussian stochastic process.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1966
\vol 11
\issue 1
\pages 120--128
\mathnet{http://mi.mathnet.ru/tvp571}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=195178}
\zmath{https://zbmath.org/?q=an:0161.14703}
\transl
\jour Theory Probab. Appl.
\yr 1966
\vol 11
\issue 1
\pages 106--113
\crossref{https://doi.org/10.1137/1111006}
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  • https://www.mathnet.ru/eng/tvp/v11/i1/p120
    Cycle of papers
    This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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