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Results tagged with inequalities
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user 56892
for questions involving inequalities, upper and lower bounds.
21
votes
2
answers
2k
views
A strange variant of the Gaussian log-Sobolev inequality
Let $\phi : \mathbb{R}^d \to \mathbb{R}$ be a convex function, and assume that it grows at most linearly at infinity for simplicity. Denote by $\gamma$ the standard Gaussian measure on $\mathbb{R}^d$, …
- 562
6
votes
Accepted
Is this simple-looking moment inequality true?
The answer is yes. Let $Y$ be an independent random variable distributed as $X$. We have
$$
\|X - \mathbb{E}[X]\|_{L^{2p}} = \|\mathbb{E}\left[X - Y \, | \, X\right]\|_{L^{2p}} \le \|X - Y\|_{L^{2p} …
- 562
7
votes
1
answer
262
views
Is this simple-looking moment inequality true?
Let $p \ge 1$ be an integer. Does there exist a constant $C_p$ such that for every random variable $X \ge 0$,
$$
\mathbb{E} \left[ \left(X - \mathbb{E} \left[ X \right] \right)^{2p} \right] \le C_p \m …
- 562