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Teor. Veroyatnost. i Primenen., 1966, Volume 11, Issue 1, Pages 120–128 (Mi tvp571)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

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

Yu. K. Belyaevab

a Moscow
b Stockholm

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.

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English version:
Theory of Probability and its Applications, 1966, 11:1, 106–113

Bibliographic databases:

Received: 13.05.1965

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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. G. Martirosyan, “Predelnaya teorema Puassona dlya chisla peresechenii nulevogo urovnya gaussovskogo statsionarnogo protsessa”, UMN, 27:3(165) (1972), 207–208  mathnet  mathscinet  zmath
    2. R. N. Miroshin, “On a Class of Multiple Integrals”, Math. Notes, 73:3 (2003), 359–369  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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