Poisson process

A counting processMathworldPlanetmath {X(t)t+{0}} is called a simple Poisson, or simply a Poisson processMathworldPlanetmath with parameter λ, also known as the intensity, if

  1. 1.


  2. 2.
  3. 3.


  4. 4.


where o(t) is the O notation.


  • The intensity λ is assumed to be a constant in terms of t.

  • Condition 3 above says that the rate in which the an event occurs once in time interval t, as t approaches 0, is λ. Condition 4 says that the event occurs more than once is very unlikely (the rate approaches zero as the time interval shrinks to zero).

  • It can be shown that X(t) has a Poisson distributionMathworldPlanetmath (hence the name of the stochastic processMathworldPlanetmath) with parameter λt:

  • Therefore, E[X(t)]=λt.

Title Poisson process
Canonical name PoissonProcess
Date of creation 2013-03-22 15:01:29
Last modified on 2013-03-22 15:01:29
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 60G51
Synonym homogeneous Poisson process
Defines simple Poisson process
Defines intensity