Poisson process

English

Etymology

From the related concept of Poisson distribution (specifying a bounded subset of the domain of a Poisson process defines a random variable that has a Poisson distribution). See also stochastic process.

Noun

Poisson process (plural Poisson processes)

1. (mathematics, statistics, probability theory) A stochastic process in which events occur continually and independently of one another.
   • 1995, Randolph Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling, Springer, page 252:

     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.

   • 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 $\lambda (t)$ of the Poisson process vary according to a stochastic process, say $\Lambda (t)$. […] 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]).

   • 2014, Oliver Ibe, Fundamentals of Applied Probability and Random Processes‎^[1], Elsevier (Academic Press), page 415:

     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.

Synonyms

• (stochastic process of continuous, independent events): Poisson point field, Poisson point process, Poisson random measure, Poisson random point field

Translations

stochastic process

• German: Poisson-Prozess m
• Hebrew: תהליך פואסון m (tahalích poasón)
• Italian: processo di Poisson m
• Japanese: ポアソン過程

See also

• carrier space