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world:forward-downward-martingale
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world:forward-downward-martingale [2026/02/07 15:02] rdouc |
world:forward-downward-martingale [2026/02/07 15:03] (current) rdouc |
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| By the monotone convergence theorem, | By the monotone convergence theorem, | ||
| $$ | $$ | ||
| - | \mathbb E[U_\infty[a,b]]<\infty, | + | \mathbb E[U_{0:\infty}[a,b]]<\infty, |
| $$ | $$ | ||
| which implies that the total number of upcrossings is almost surely finite. | which implies that the total number of upcrossings is almost surely finite. | ||
world/forward-downward-martingale.txt · Last modified: 2026/02/07 15:03 by rdouc
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