Example 6.2 (The Poisson Process) Consider a birth and death process for which n = 0, for

Example 6.2 (The Poisson Process) Consider a birth and death process for which

μn = 0, for all n  0

λn = λ, for all n  0 This is a process in which departures never occur, and the time between successive arrivals is exponential with mean 1/λ. Hence, this is just the Poisson process. 

A birth and death process for which μn = 0 for all n is called a pure birth process. Another pure birth process is given by the next example.