Birth process

For the biological process, see birth.
birth process
A birth process with birth rates .

In probability theory, a birth process or a pure birth process[1] is a special case of a continuous-time Markov process and a generalisation of a Poisson process. It defines a continuous process which takes values in the natural numbers and can only increase by one (a "birth") or remain unchanged. This is a type of birth–death process with no deaths. The rate at which births occur is given by an exponential random variable whose parameter depends only on the current value of the process

  1. ^ Upton & Cook (2014), birth-and-death process.