Finite Point Processes

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Abstract

The Poisson process can be generalized in many directions. We have already discussed some consequences of relaxing the independency assumptions while retaining those of stationarity and orderliness of a point process on the line. In this chapter we examine generalizations in another direction, stemming from the observation in Chapter 2 that, for a Poisson process, conditional on the total number of points in a bounded region of time or space, the individual points can be treated as independently and identically distributed over the region. This prompts an alternative approach to specifying the structure of point processes in a bounded domain or, more generally, of any point process in which the total number of points is finite with probability 1. Such a process is called a finite point process.