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Line 19: Then there is a sequence of stopping times ''τ''<sub>1</sub> ≤ ''τ''<sub>2</sub> ≤ ... such that the <math>W_{\tau_{n}}</math> have the same joint distributions as the partial sums ''S''<sub>''n''</sub> and ''τ''<sub>1</sub>, ''τ''<sub>2</sub> − ''τ''<sub>1</sub>, ''τ''<sub>3</sub> − ''τ''<sub>2</sub>, ... are independent and identically distributed random variables satisfying :<math>\mathbb{E}[\tau_{n} - \tau_{n - 1}] = \mathbb{E}[X_{1n}^{2}]</math> and :<math>\mathbb{E}[(\tau_{n} - \tau_{n - 1})^{2}] \leq 4 \mathbb{E}[X_{1n}^{4}].</math> ==References==

Skorokhod's embedding theorem: Difference between revisions