For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.
The Poisson process is one of the most widely used point processes, as well as one of the most important objects of study in the theories of point processes and of (more general) stochastic processes. Its name is derived from the fact that, for a Poisson point process, the number of points in a region of finite size is a random variable with a Poisson distribution.
The Poisson process can be defined on many different types of spaces. The simplest definition occurs on the real line, where the distance between two consecutive points of the process will have an exponential distribution. This implies that the points have the memoryless property: intuitively, the process "restarts afresh" at every point.