A Study of Stationary Point Processes and Their Passages Through Memoryless Systems

摘要

A stationary point process is a sequence of points distributed along the time axis. The locations of these points are governed by probability laws which are invariant under time translation. In the investigation a special class of stationary point processes is defined, called the class with factorable regression. This definition is based on a definition used by Nuttall. For this class the regression function of the cumulative number of points is evaluated in a specific form. Considered as a function of a given number of points in a specified interval, this regression is linear. If a process with a factorable regression is the input to a memoryless system, then the regression of the output with respect to the input is also factorable. Conversely, if the output of a memoryless system has factorable regression with respect to the input, then the input process itself must have factorable regression. The memoryless system is defined by the special requirement that the conditional expectation of the number of output points in a specified interval, given the locations of all the input points, must depend only on the number of input points which have occurred in the same interval. (Author)