Binomial process

A binomial process is a special point process in probability theory.

Definition

Let be a probability distribution and be a fixed natural number. Let be i.i.d. random variables with distribution, so for all.
Then the binomial process based on n and P is the random measure
where

Properties

Name

The name of a binomial process is derived from the fact that for all measurable sets the random variable follows a binomial distribution with parameters and :

Laplace-transform

The Laplace transform of a binomial process is given by
for all positive measurable functions.

Intensity measure

The intensity measure of a binomial process is given by

Generalizations

A generalization of binomial processes are mixed binomial processes. In these point processes, the number of points is not deterministic like it is with binomial processes, but is determined by a random variable. Therefore mixed binomial processes conditioned on are binomial process based on and.

Literature

Category:Point processes