Skorokhod's representation theorem
The Skorokhod representation, named after the Ukrainian mathematician Anatoli Skorokhod, is a set from the field of probability theory. It establishes a relationship between two different convergence concepts.
Statement
Let and be random variables, so that converge in distribution to: . Then there is a probability space and random variables defined thereon and with:
- , That is, and and and have the same distribution, and
- Which converge to almost certain.
They can thus be without prejudice to their distributions replaced by almost sure convergent random variables.