Timeline for Convergence in probability of series of random variables
Current License: CC BY-SA 4.0
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| May 23 at 12:07 | comment | converted from answer | Pierfrancesco Alaimo Di Loro | in your example, the convergence to 1 occurs because as $n$ increases there is an increasing number of $X_{\ell, n}= 1$. I think this sort of situation can only happen if the double limit is not $0$. What I mean is that, in your example, $X_{\ell, n}\rightarrow 1$ for both $\ell$ and $n$ approaching infinity. What if we further assume that $X_{\ell, n}\rightarrow 0$ for both $\ell$ and $n$ approaching infinity? | |
| Sep 9, 2021 at 19:12 | history | answered | Yuval Peres | CC BY-SA 4.0 |