Skorokhod's Embedding Theorem refers to either or both of two results of probability theory, named for the Ukrainian mathematician A. V. Skorokhod, that allow a suitable collection of random variables to be represented as a Wiener process, or Brownian motion, sampled at an associated collection of stopping times. The theorem is a foundational tool for transferring facts proved about Brownian motion to more general random walks and martingales.
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StatementFor a real-valued random variable X with mean zero and finite variance, there is a stopping time for a standard Wiener process W such that the process at that stopping time has the same distribution as X. 1 Classification
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Source Skorokhod's embedding theorem (Wikipedia)
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1. Skorokhod's embedding theorem (Wikipedia)
Skorokhod's first embedding theorem section
Let X be a real-valued random variable with expected value 0 and finite variance; let W denote a canonical real-valued Wiener process. Then there is a stopping time (with respect to the natural filtration of W), τ, such that Wτ has the same distribution as X
In Branch: Probability and Statistics, Lead sentence
In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard an
In Group: Stochastic Processes and Martingales, Lead section
collection of random variables as a Wiener process (Brownian motion) evaluated at a collection of stopping
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