Skorokhod's embedding theorem: Difference between revisions

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In [[mathematics]] and [[probability theory]], '''Skorokhod's embedding theorem''' is either or both of two [[theorem]]s that allow one to regard any suitable collection of [[random variable]]s as a [[Wiener process]] ([[Brownian motion]]) evaluated at a collection of [[stopping time]]s. Both results are named for the [[Ukraine|Ukrainian]] [[mathematician]] [[Anatoliy Skorokhod|A. V. Skorokhod]].

==Skorokhod's first embedding theorem==

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and

:<math>\operatorname{E}[(\tau_{n} - \tau_{n - 1})^2] \leqle 4 \operatorname{E}[X_1^4].</math>

==References==

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* {{cite book | last=Billingsley | first=Patrick | title=Probability and Measure | publisher=John Wiley & Sons, Inc. | ___location=New York | year=1995 | isbn=0-471-00710-2}} (Theorems 37.6, 37.7)

[[Category:ProbabilityTheorems theoremsin probability theory]]

[[Category:Wiener process]]

[[Category:Ukrainian inventions]]