Skorokhod embedding theorem
= Skorokhod embedding theorem
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The Skorokhod embedding theorem represents a centered <probability distribution> $\mu$ on the <real numbers> with finite <variance> as $B_T\sim\mu$ for a <stopping time> $T$ of <Brownian motion>. One may choose $T$ so that the stopped process $(B_{t\wedge T})$ is <uniform integrability>[uniformly integrable] and $\mathbb ET=\int x^2\mu(dx)$.