This article is cited in 8 papers

Convergence of the Longuet-Higgins series for Gaussian stationary Markov process of the first order

R. N. Mirošin

A. A. Ždanov Leningrad State University

Abstract: Let $\biggl(\xi_t,\frac{d\xi_t}{dt}\biggr)$ be a Gaussian stationary Markov process. M. S. Longuet-Higgins used alternating series (coefficients of which are expressed in terms of factorial moments of the number of zeroes of $\xi_t$) for a representation of the distribution function of the distance between the $i^{th}$ and the $(i+m+1)^{th}$ zeroes of $\xi_t$. In this paper the problem of convergence of these series is studied.

Received: 03.10.1978

 English version: Theory of Probability and its Applications, 1981, 26:1, 97–117

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