Simulation methods for Poisson processes in nonstationary systems
By: by Peter A. W. Lewis and Gerald S. Shedler
Contributors: Shedler, Gerald S.; Naval Postgraduate School (U.S.)
Publisher: Naval Postgraduate School
Published: 1978
Place of publication: Monterey, California
Language: eng
Number of pages: 25
Subjects: Stochastic processes; Point processes; Poisson processes
Description: The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the rate or intensity of occurrence of points varies, usually with time. The process has the characteristic properties that the number of points in any finite set of nonoverlapping intervals are mutually independent random varialbes, and that the number of points in any of these intervals has a Poisson distribution. This paper first discusses several general methods for simulation of the one-dimensional nonhomogeneous Poisson process. Then a particular and very efficient method for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the nonhomogeneous Poisson process to the gap statistics from a random number of exponential random variables with suitably chosen parameters. Finally, a simple and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is applicable for any given rate function and is based on controlled deletion of points in a Poisson process with a rate function that dominates the given rate function.
Notes: Title from cover.

"NPS55-78-019"--Cover.

"August 1978"--Cover.

Includes bibliographical references (p. 9).

"Approved for public release; distribution is unlimited"--Cover.

Technical report; 1978.

ck/ 7/15/09.