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Results tagged with inequalities
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user 489044
for questions involving inequalities, upper and lower bounds.
0
votes
0
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151
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Inequalities on the distribution of the maximum of the normalized sum $\max_{k = 1,\dots,n} ...
Let $\{X_i\}_{i\in\mathbb{N}}$ be i.i.d. random variables with $\mathbb{E}(X) = 0$,$\mathbb{E}(X^2) = \sigma^2$ and finite moments. Let $S_k = \sum_{i = 1}^{k} X_i$ and consider the normalized quantit …
- 63
2
votes
1
answer
365
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A maximal inequality
Let $\{X_i\}_{i\in\mathbb{N}}$ be i.i.d. symmetric random variables, with $-1\leq X_i\leq 1$, $\mathbb{E}(X_i) =0$, $\mathbb{E}(X_i^2) = 1$. We have that:
$$
P\left(\bigcap_{k = 1}^{n}\frac{|\sum_{i = …
- 63