What does it it mean to say a martingale is closed [in layman terms] ? Does it just mean the martingale converges ??
What does it mean to say a martingale is closed?
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martingales
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0Where did you encounter this? – 2012-11-28
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A martingale $(X_n,\mathcal{F}_n)_n$ is called (right-)closable if there exists a random variable $X$ such that $X_n = \mathbb{E}(X|\mathcal{F}_n)$. (A sufficient condition is that $(X_n)_n$ is uniformly integrable.)