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Results tagged with limits-and-convergence
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user 23959
Convergence of series, sequences and functions and different modes of convergence.
1
vote
1
answer
108
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Convergence in probability of sample covariance for permutation invariant triangular arrays
Take two triangular arrays $X_{N,i}$ and $Y_{N,i}$ of random variables where $1 \le i \le N$. Suppose that the families $\{X_{N,i}\}$ and $\{Y_{N,i}\}$ are independent, and that the following conditio …
- 128k
2
votes
1
answer
378
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Law of large numbers for triangular arrays whose moments "look independent"
Let $(X_{n,k})_{k=1,\ldots,n}^{n\in\mathbb{N}}$ be a triangular array of random variables with finite moments of all orders, with no assumptions on their independence. Suppose that
$$
\mathbb{E}\left[ …
- 3,993