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Results tagged with pr.probability
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user 163533
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
1
answer
357
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Proof of "Prove that a sub-gaussian and isotropic random vector over a finite set T implies ...
Here the original question was asked and answered. However I have a question to the solution. If I get it right they try to show $\frac 12 I_n \leq \mathbf{E} YY^T \leq I_n$ by proving
$$ \mathbf{E} \ …
- 115
3
votes
1
answer
729
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Uniform distribution in Ball with radius $\sqrt{n}$ is sub-gaussian
I have to show that a random vector $X$ who ist uniformly distributed on the Ball with Radius $\sqrt{n}$ is sub-gaussian with
$$\lVert X \rVert_{\psi_2}\leq C$$
I already know that the same result doe …
- 115
0
votes
1
answer
354
views
Random variable is Big O in probability notation
Let $R_n$ be a random variable with values in $[0,1]$ and $nR_n$ converges to $\frac{1}{1+C} \chi_m^2$ in distribution for some constant $C>0$ and $m\in \mathbb{N}$. Is it possible to show that $(1-R_ …
- 115
5
votes
1
answer
480
views
Concentration inequality for Hilbert space valued random variables
I have read in a paper about the following result:
Let $V$ be a separable Hilbert space and $(\Omega,A_{\Omega},P)$ a probability space. Suppose that $Y_1,Y_2,...$ is a sequence of independent $V$-val …
- 115