Some Extensions of the Erd\"{o}s-R\'{e}nyi Law of Large Numbers (Yuri Kifer, Hebrew University, Israel)

23.02.2017 16:15

Let $X_1, X_2, \ldots$ be i.i.d. random variables. Erd\"{o}s and R\'{e}nyi proved in 1970 what they called a new law of large numbers for sums $\Sigma_n=\sum_{1\le i\le n}X_i$ which says that with probability one,\[I(\beta)\lim_{ \to\infty}\max_{0\le m\le n-\lfloor\frac{\ln n}{I(\beta)}\rfloor}\frac{\Sigma_{m+\lflo\frac{\ln n}{I(\beta)}\rfloor}-\Sigma_m}{\ln n}=\beta\] provided $I(\beta)

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Room 17

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Section de mathématiques

Intervenant-e-s

Yuri Kifer, Hebrew University, Israel

entrée libre

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Catégorie: Colloque