Poisson process

plural Poisson processes

1. mathematicsA stochastic process in which events occur continually and independently of one another.

   University buses arrive at the Students Center to take students to their classes according to a Poisson process with an average rate of 5 buses per hour.

   2014, Oliver Ibe, Fundamentals of Applied Probability and Random Processes, Elsevier (Academic Press), page 415

   2 more examples

   These properties are readily apparent when one considers that the Poisson process is derived from the binomial processes, which, as seen in Section 6.1, can be viewed in terms of coin tosses.

   1995, Randolph Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling, Springer, page 252

   2012, Peter Guttorp, Thordis L. Thorarinsdottir, Chapter 4: Bayesian Inference for Non-Markovian Point Processes, Emilio Porcu, José–María Montero, Martin Schlather (editors), Advances and Challenges in Space-time Modelling of Natural Events, Springer, Lecture Notes in Statistics 207, page 88, The doubly stochastic Poisson process, introduced by Cox in [9] and so named by Bartlett in [6] is obtained by letting the rate λ(t) of the Poisson process vary according to a stochastic process, say Λ(t). […] There are instances of doubly stochastic Poisson processes that are identical to cluster processes (for example, the shot noise process driven by a stationary Poisson process is identical to a Neyman-Scott Poisson cluster process, see p.171-172 in [12]).

   Synonyms: Poisson point field, Poisson point process, Poisson random measure, Poisson random point field