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I've had that sig on other scoop sites, before they had picture embedding macros, and I've kept it for sentimental reasons :)

It's a piece of LaTeX which represents the defining property of a martingale.

The simplest example of a martingale in this sense is a double or nothing gambling strategy in certain games of chance(*), but a better way of understanding them is that they are purely random processes, which cannot be predicted based on historical observations: if you try to predict their future, your best guess is to duplicate the present, regardless of what you've seen in the past.

(*)wherein one proves that double or nothing fails to help one win: when the strategy has no statistical trend, then there is no advantage from using it.

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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Sun Aug 17th, 2008 at 03:44:38 AM EST
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