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Results tagged with pr.probability
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user 174236
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
1
answer
263
views
Bound on the distribution of a ratio involving Gaussian distributions
Let $U \sim \mathcal{N}(0, I_K)$ be a Gaussian vector of dimension $K$ and $V \sim \mathcal{N}(0,1)$, independent of $U$. Let $\Delta$ be a diagonal matrix with non-negative diagonal elements, $c\in\m …
- 197
2
votes
How to demonstrate a correlation inequality?
The inequality does not always hold. Let $D \sim$ Bernoulli$(p)$, independent of $Y$. Let $Y'$ and $Y''$ be two independent copies of $Y$ (also independent of $Y$). Let $X=D Y+(1-D) Y'$ and $Z=DY'' + …
- 197
2
votes
1
answer
136
views
Comparison between $\|X\|_2$ and $\|X\|_{2,1}$
For any real random variable $X$, define
$$\|X\|_{2,1}=\int_0^\infty \sqrt{\Pr(|X|>t)}dt.$$
This quantity (it is not a norm) appears in various problems, e.g. the multiplier central limit theorem (see …
- 197
2
votes
1
answer
100
views
Inequality for Gaussian measures
Let $\mu$ denote a centered Gaussian measure on $\mathbb{R}^k$, $K=(-\infty, a] \times \mathbb{R}^{k-1}$ ($a\ge 0$) and $L=\mathbb{R}\times C$ where $C$ is a convex set in $\mathbb{R}^{k-1}$, symmetri …
- 197