Simulation of Nonhomogeneous Poisson Processes with Degree-Two Exponential Polynomial Rate Function

A new method for simulating a nonhomogeneous Poisson process with rate function λ(t) = exp{α 0 + α 1 t + a 2 t 2 } in a fixed time interval (0, t 0 ] is given. The method is based on a decomposition of the process, it employs a rejection technique, in conjunction with a method for simulating the nonhomogeneous Poisson process with rate function exp {γ 0 + γ 1 t} by generation of gap statistics from a random number of exponential random variables with suitably chosen parameters. The proposed method for the degree-two exponential polynomial model is more efficient than time-scale transformation of a homogeneous Poisson process, and should be applicable to other rate function models.