# Optional stopping theorem for Hilbert valued martingales

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? – Nate Eldredge Jun 28 '11 at 3:18
@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! – mellow Jun 30 '11 at 21:28
@mellow If you're still looking for an answer, perhaps edit the question to include your attempt. – Ben Derrett Jan 15 '12 at 21:46