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[[File:lighterstill.jpg]][[File:Renewal.jpg|right|frame]]
[[File:lighterstill.jpg]][[File:Hornbill_Renewal.jpg|right|frame]]
*Pronunciation - \ri-ˈnü-əl, -ˈnyü-\
\ri-ˈnü-əl, -ˈnyü-\
*Origins - circa 1686
circa 1686
==Definitions==
==Definitions==
# : the [[act]] or [[process]] of renewing : repetition
# : the [[act]] or [[process]] of renewing : repetition
# : the rebuilding of a large area (as of a city) by a [[public]] [[authority]]
# : the rebuilding of a large area (as of a city) by a [[public]] [[authority]]
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<center>For lessons on the [[topic]] of '''''Renewal''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Renewal this link].</center>
==Poisson Process==
A '''Poisson process''', named after the French mathematician [https://en.wikipedia.org/wiki/Sim%C3%A9on-Denis_Poisson Siméon-Denis Poisson] (1781–1840), is a [https://en.wikipedia.org/wiki/Stochastic_process stochastic] [[process]] in which [[events]] occur continuously and [[independently]] of one another (the word [[event]] used here is not an instance of the [[concept]] of event frequently used in [[probability]] [[theory]]). Examples that are well-[[modeled]] as Poisson processes include the radioactive decay of [[atoms]], telephone calls arriving at a switchboard, page view requests to a website, and rainfall.
The Poisson process is a collection {N(t) : t ≥ 0} of [https://en.wikipedia.org/wiki/Random_variable random variables], where N(t) is the [[number]] of [[events]] that have occurred up to time t (starting from time 0). The number of events between time a and time b is given as N(b) − N(a) and has a [https://en.wikipedia.org/wiki/Poisson_distribution Poisson distribution]. Each [[realization]] of the [[process]] {N(t)} is a non-negative integer-valued step function that is non-decreasing, but for [[intuitive]] [[purposes]] it is usually easier to think of it as a point [[pattern]] on [0,∞) (the points in time where the step function jumps, i.e. the points in time where an event occurs).
The Poisson process is a continuous-time process: its discrete-time [[Complement|counterpart]] is the [https://en.wikipedia.org/wiki/Bernoulli_process Bernoulli process]. Poisson processes are also examples of [https://en.wikipedia.org/wiki/Continuous-time_Markov_process continuous-time Markov processes]. A Poisson process is a [[pure]]-[[birth]] [[process]], the [[simplest]] example of a birth-[[death]] process. By the aforementioned [[interpretation]] as a [[random]] point pattern on [0, ∞) it is also a point process on the real half-line.[https://en.wikipedia.org/wiki/Poisson_process]
[[Category: General Reference]]
[[Category: General Reference]]
