On the number of intersections of a level by a Gaussian stochastic process. I
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 1, pp. 120-128
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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.