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→Skorokhod's first embedding theorem: Repairing links to disambiguation pages - You can help! using AWB |
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==Skorokhod's first embedding theorem==
Let ''X'' be a [[real number|real]]-valued random variable with [[expected value]] 0 and [[Wikt:finite|finite]] [[variance]]; let ''W'' denote a canonical real-valued Wiener process. Then there is a stopping time (with respect to the natural [[filtration (abstract algebra)|filtration]] of ''W''), ''τ'', such that ''W''<sub>''τ''</sub> has the same distribution as ''X'',
:<math>\mathbb{E}[\tau] = \mathbb{E}[X^{2}]</math>
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