ZERO-CROSSING INTERVALS OF ENVELOPES OF GAUSSIAN PROCESSES.
JOHNS HOPKINS UNIV BALTIMORE MD CARLYLE BARTON LAB
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This paper generalizes some theoretical results concerning the zero-crossing intervals of both Gaussian processes and envelopes of Gaussian processes. Some new experimental results concerning the zero-crossing intervals of both types of processes are also presented. It is shown that probabilities and probability densities defined by the zero-crossing points of an envelope process are similar to the corresponding probabilities and probability densities defined by the zerocrossing points of an associated Gaussian process. At present none of the probabilities or probability densities can be derived explicitly by analytical methods. The standard deviations of the zero-crossing intervals are also presented. In the case of the associated Gaussian process, the correlation coefficient for two successive zero-crossing intervals is presented. The first moments of the probability densities are compared with the exact theoretical values. All the other experimental results are compared with theoretical approximations. The statistical dependence between two successive axis-crossing intervals is investigated. Author