ABSTRACT
In this chapter we study a simple way by which a positive-going continuous random variable can be associated with discrete events. In this model, events are triggered randomly at a rate that is governed by the magnitude of the variable. Thus we start by assuming that a ‘variable’ of constant magnitude will generate a proportionate constant rate of purely random and uncorrelated events. The number of events in a given time interval will then be Poisson distributed with a mean that is equal to the event rate multiplied by the counting time. When the variable changes sufficiently slowly with time it is assumed that the event rate follows suit, generating a Poisson series of events with a locally varying mean value. A model that combines a random Poisson series of events and a continuous random variable in this way is called a doubly stochastic Poisson process (Figure 9.1).
