Wave-Length and Amplitude for a Stationary Process after a High Maximum: Decreasing Covariance Function.
NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
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The paper is a direct continuation of the paper Wave-length and amplitude for a stationary process after a high maximum, this series No. 742. It deals with the limiting properties as u approaches infinity of wave-length tau sub u and amplitude delta sub u after a local maximum with height u in a stationary normal process. It is assumed that the covariance function rt is strictly decreasing for t 0. The limiting distribution of tau sub u is derived and expressed by means of a certain time transformation and it includes a slight generalization of the Poisson limit theorem for crossings of a very high level. Especially it is shown that tau sub u approaches infinity and that delta sub uu approaches 1 as u approaches infinity. Author
- Statistics and Probability