The Poisson Process and Its Ramifications

Abstract

We begin by describing in an informal fashion the subject matter of this chapter. The part of the general theory of stochastic processes dealing with countable sets of points randomly distributed on the real line or in an arbitrary space (for instance, Cartesian d-dimensional space) is called the “Theory of Point Processes.” Of all point processes, those on the real line have been most widely studied. Notwithstanding their relatively simple structure, they form building blocks in a variety of industrial, biological, geophysical, and engineering applications. The following example describes a general situation which in a natural fashion introduces a point process on a line.KeywordsArrival TimeMarkov ProcessPoisson ProcessPoint ProcessMarkov PropertyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.