Abstract
Summary A stationary point process being supposed characterized by the counts Xl of events in time intervals of equal length l, a discussion is given of relationships, valid for a wide class of processes, between the variance-time function var Xl, the autocorrelation function of the Xl-series, and the autocovariance density. “Controlled variability” processes are then defined and discussed. A study is made of particular controlled variability processes, “(a, b) processes”, in which events occur at times a 0 + ia + bi, the bi being independent identically distributed random variables. In particular, it is shown that the autocovariance density for an (a, b) process is proportional to the convolution probability density of the difference of two independent bi's, with a closely related result for the autocorrelation function of counts.
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