Proposition 5.3.5. Suppose {Xn} is a martingale of uniformly bounded differ- ences. That is, almost surely sup, Xn-Xn-1

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Proposition 5.3.5. Suppose {Xn} is a martingale of uniformly bounded differ- ences. That is, almost surely sup, Xn-Xn-1

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Proposition 5 3 5 Suppose Xn Is A Martingale Of Uniformly Bounded Differ Ences That Is Almost Surely Sup Xn Xn 1 1
Proposition 5 3 5 Suppose Xn Is A Martingale Of Uniformly Bounded Differ Ences That Is Almost Surely Sup Xn Xn 1 1 (16.18 KiB) Viewed 54 times
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Proposition 5.3.5. Suppose {Xn} is a martingale of uniformly bounded differ- ences. That is, almost surely sup, Xn-Xn-1 ≤ c for some finite non-random constant c. Then, P(AUB) = 1 for the events A = {w: lim X, (w) erists and is finite}, 814x B = {w: lim sup X₁ (w) = ∞ and lim inf X₁ (w) = -∞}. 71-X 818
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