Sum of independent random variables

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Convergence of Moments of Random Sums of Independent Random Variables

Theory of Probability & Its Applications, 1986
Translation from Teor. Veroyatn. Primen. 30, No.2, 361-364 (Russian) (1985; Zbl 0572.60034).
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On the Increase of Dispersion of Sums of Independent Random Variables

Theory of Probability & Its Applications, 1961
Let $\xi _1 ,\xi _2 , \cdots ,\xi _n $ be independent random variables, \[ Q_k \{ l \} = \mathop {\sup }\limits_x {\bf P} \{ x \leqq \xi _k \leqq x + l \}, \]\[ Q(L) = \mathop {\sup }\limits_x {\bf P} \{ {x \leqq \xi _1 + \cdots + \xi _n \leqq x + L} \},\quad s = \sum\limits_{k + 1}^n {( {1 - Q_k (l_k )} )l_{k^2 } } \]We prove:Theorem 1.
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Sums of Independent Random Variables.

Journal of the Royal Statistical Society. Series A (General), 1976
A. D. Barbour, V. V. Petrov, A. A. Brown
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On a Property of Sums of Independent Random Variables

Theory of Probability & Its Applications, 1978
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On the oscillations of sums of independent random variables

The Annals of Mathematics, 1970
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Sums of independent random variables

2022
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An Inequality for Sums of Independent Random Variables

Proceedings of the London Mathematical Society, 1945
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Estimating the distribution of a sum of independent lognormal random variables

IEEE Transactions on Communications, 1995
Norman C Beaulieu
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