@MISC{Pasupathy_generatingnonhomogeneous, author = {Raghu Pasupathy}, title = {Generating Nonhomogeneous Poisson Processes}, year = {} }

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Abstract

We present an overview of existing methods to generate pseudorandom numbers from a nonhomogeneous Poisson process. We start with various definitions of the nonhomogeneous Poisson process, present theoretical results (sometimes with a proof) that form the basis of existing generation algorithms, and provide algorithm listings. Whenever available, we also provide links to sources containing computer codes. With the intent of guiding users seeking an appropriate algorithm for a given setting, we emphasize computationally burdensome operations within each algorithm. Our treatment includes both one-dimensional and two-dimensional Poisson processes. Key words: statistics; simulation; random process generation; Poisson processes. Recall that a counting process {Nt, t ≥ 0} is a stochastic process defined on a sample space Ω such that for each ω ∈ Ω, the function Nt(ω) is a “realization ” of the number of “events ” happening in the interval (0, t], with N0(ω) = 0. By this definition, Nt(ω) is automatically integer valued, non-decreasing, and right-continuous for each ω. A nonhomogeneous Poisson process is a type of counting process that is characterized as follows. Definition 1. A counting process {Nt, t ≥ 0} is called a nonhomogeneous Poisson process if: (i) ∀t, s ≥ 0, and 0 ≤ u ≤ t, Nt+s − Nt is independent of Nu;