Proposition 5.3.5. Suppose {Xn} is a martingale of uniformly bounded differ- ences. That is, almost surely sup, Xn-Xn-1
Posted: Wed May 04, 2022 9:34 am
- 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 55 times
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