View source for Convergence of random variables

In [[probability theory]], there exist several different notions of '''convergence of random variables'''.

== Description ==

The [[Limit of a sequence|convergence of sequences]] of [[Random variable|random variables]] to some limit [[random variable]] is an important concept in [[probability theory]], and its applications to [[statistics]] and [[Stochastic process|stochastic processes]].

The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.

The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.

== See also ==

* [[Asymptotic distribution]]
* [[Big O in probability notation]]
* [[Continuous stochastic process]] - the question of continuity of a stochastic process is essentially a question of convergence, and many of the same concepts and relationships used above apply to the continuity question.
* [[Convergence of measures]]
* [[Limit of a sequence]]
* [[Proofs of convergence of random variables]]
* [[Skorokhod's representation theorem]]
* [[Tweedie distribution]]

== External links ==

* [https://en.wikipedia.org/wiki/Convergence_of_random_variables Convergence of random variables] @ Wikipedia


[[Category:Mathematics]]
[[Category:Probability]]