A binomial process is a special point process in probability theory.
be a probability distribution and
be a fixed natural number.
random variables with distribution
Then the binomial process based on n and P is the random measure where
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
: The Laplace transform of a binomial process is given by for all positive measurable functions
The intensity measure
of a binomial process
is given by 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