Poisson process

A Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object that consists of points randomly located on a mathematical space. The process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous discipline.

The Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process.

Formalization

Main properties:

• ${\displaystyle P{N=n}={\frac {\Lambda ^{n}}{n!}}e^{-\Lambda }}$
• Complete independence

See also

Wiener process, Levy process, Gamma process, Markov process

Books

• Kingman, John Frank (1992). Poisson processes. Claredon Press.