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Results tagged with pr.probability
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user 481055
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
2
votes
1
answer
134
views
Linear transformation of random vector has bounded moments?
Suppose that the random vector $\mathbf{y}=(Y_1, Y_2,\ldots, Y_p)^{\top}$ satisfies:
$\mathbb{E}(Y_i) = 0$, $\mathbb{E}(Y_i^2)=1$ for any $1\leqslant i \leqslant p$;
$\mathrm{Cov}(Y_i,Y_j)=0$ for $i\ …
- 81
5
votes
1
answer
282
views
Maximal inequality of iid random variables $\{X_{ij}\}_{1\leqslant i,j \leqslant n}$
Suppose that $\{X_{ij}\}_{1\leqslant i,j\leqslant n}$ are iid random variables with $\mathbb{E}(X_{11})=0$ and $\mathrm{Var}(X_{11})=1$, does the following convergence hold:
$$
\max_{1\leqslant j\le …
- 81