This article is cited in 33 papers

Short Communications

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

Yu. K. Belyaev<sup>ab

a</sup> 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.

Received: 13.05.1965

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

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