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Suppose $X_n$ is a Hilbert-valued martingale. Does the optional sampling theorem apply in this case? Does anyone know where I can find a proof?

Thank you.

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    I don't know a reference offhand, but have you tried proving it yourself? It seems like it should be straightforward. If not, what goes wrong?2011-06-28
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    @NateElderedge Thank you, I agree that it should be straightforward but I am often surprised by the subtle problems appearing in infinite dimension. Thanks again!2011-06-30
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    @mellow If you're still looking for an answer, perhaps edit the question to include your attempt.2012-01-15

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