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16 thg 10, 2021 · The problem is as below. Suppose $EX_i=0$ and $E\exp (\theta X_i)=\infty$ for all $\theta>0$. Let $S_n=X_1+\dots+X_n$. Then $$\frac {1} {n}\log P (S_n \geq na) \rightarrow …
21 thg 10, 2023 · I was studying Durrett's proof of Strong Law of Large numbers and I got stuck while trying to understand the following Lemma: Let $X_1,X_2,\dots$ be pairwise independent …
27 thg 2, 2019 · In Durrett's Probability (4th edition), an example of a tail event (an event in the tail sigma-field $\bigcap_n \sigma (X_n, X_ {n+1}, \dots)$) is the following: given independent …
5 thg 2, 2012 · It seems like they use Kronecker's lemma (Theorem 2.5.9) at the end but I do not quite understand ...
17 thg 11, 2022 · I am interested in this problem by Durret in Probability: Theory and Examples. Let X1,X2, … X 1, X 2, be i.i.d. and not ≡ 0 ≡ 0. If E|X1| <∞ E | X 1 | <∞, show that lim sup n→∞ …
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