Poisson Processes

Abstract

The Poisson distribution rivals the normal distribution in importance. It occupies this position of eminence because of its connection to Poisson processes [59, 60, 80, 96, 106, 114, 170]. A Poisson process models the formation of random points in space or time. Most textbook treatments of Poisson processes stress one-dimensional processes. This is unfortunate because many of the important applications occur in higher dimensions, and the underlying theory is about as simple there. In this chapter, we emphasize multidimensional Poisson processes, their transformation properties, and computational tools for extracting information about them.