In
probability theory, there exist several different notions of
convergence of random variables. The
convergence of
sequences of
random variables to some
limit random variable is an important concept in probability theory, and its applications to
statistics and
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 behaviour that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behaviour can be characterised: two readily understood behaviours 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.