In probability theory, Donsker's theorem, named after M. D. Donsker, identifies a certain stochastic process as a limit of empirical processes. It is sometimes called the functional central limit theorem.
A centered and scaled version of empirical distribution function Fn defines an empirical process
indexed by x ∈ R.
Theorem (Donsker, Skorokhod, Kolmogorov) The sequence of Gn(x), as random elements of the Skorokhod space, converges in distribution to a Gaussian process G with zero mean and covariance given by
The process G(x) can be written as B(F(x)) where B is a standard Brownian bridge on the unit interval.
Read more about Donsker's Theorem: History
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“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)