Simulation and Modelling - Old Questions

6. What is non-stationary Poisson process? How can we convert it into a stationary Poisson process?

The non-stationary Poisson process is a Poisson process for which the arrival rate varies with time. More specifically, it can be defined as follows:

The counting process N(t) is a non-stationary Poisson process if:

a) The process has independent increments.

b) 

    Where, λ(t) = the arrival rate at time t

                dt = differential sized interval

The definition is identical to the stationary Poisson process, with the exception that the arrival rate, λ(t), is now a function of time.

A counting process N(t) is a stationary Poisson process with rate  λ if

a) The process has independent increments.

b) The process has stationary increments. and

c) 

A non-stationary Poisson process can be transformed into a stationary Poisson process with arrival rate 1.