Poisson Process

A Poisson process is a special type of counting process. There are several ways to characterize the Poisson process. One can focus on the number of events that occur in fixed intervals, when events occur, and the times between those events, or the probabilistic behavior of individual events on infinitesimal intervals. This leads to three equivalent definitions of a Poisson process, each of which gives special insights into the stochastic model. The exponential distribution plays a central role in the Poisson process. The thinned process is the superposition process obtained by merging, or adding, independent Poisson processes. If a Poisson process contains exactly n events in an interval [0, t], then the unordered locations, or times, of those events are uniformly distributed on the interval. The spatial Poisson process is a model for the distribution of events, or points, in two or higher-dimensional space.