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Then you are measuring the wrong quantity, no? The winner isn't the fastest in the water, it's the first who hits the plate at the finish line. How you get there is irrelevant, although you obviously have to be fast enough through the water to make it.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Tue Aug 26th, 2008 at 01:04:08 AM EST
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