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# A remark on stable sequences of random variables and a limit distribution theorem for a random sum of independent random variables

Acta Mathematica Hungarica
Author: J. Mogyoródi
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# On some rate of convergence questions

Studia Scientiarum Mathematicarum Hungarica
Author: Dao Tuyen

Hanson, D. L. and Wright, F. T. , Some Convergence Results for Weighted Sums of Independent Random Variables, Z. Wahrscheinlichkeitstheor. Verw. Geb. , 19 (1971), 81–89. MR 45 #1220 Wright F. T

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# One-sided strong laws forincrements of sumsof i.i.d. random variables

Studia Scientiarum Mathematicarum Hungarica
Author: A. N. Frolov

4 PETROV, V.V., On the probabilities of large deviations for sums of independent random variables, Teor. Verojatnost. i Primenen. 10 (1965), 310-322 (in Russian). MR 32

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# A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica
Author: Alexander Pruss

## Abstract

Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$S_n = X_1 + \cdot \cdot \cdot + X_n$$ \end{document}
. Under some conditions on the positive sequence τ n and the positive increasing sequence a n, we give necessary and sufficient conditions for the convergence of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\nolimits_{n = 1}^\infty {\tau _n } P\left( {\left| {S_n } \right| \geqslant \varepsilon an} \right)$$ \end{document}
for all & > 0, generalizing Baum and Katz's~(1965) generalization of the Hsu–Robbins–Erds (1947, 1949) law of large numbers, also allowing us to characterize the convergence of the above series in the case where τn = n -1and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$an = \left( {n\log n} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}$$ \end{document}
for n ≤ 2, thereby answering a question of Spătaru. Moreover, some results for non-identically distributed independent random variables are obtained by a recent comparison inequality. Our basic method is to use a central limit theorem estimate of Nagaev (1965) combined with the Hoffman-Jrgensen inequality~(1974).
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# On the asymptotic independent representations for sums of some weakly dependent random variables

Studia Scientiarum Mathematicarum Hungarica
Authors: Rafik Aguech, Sana Louhichi, and Sofyen Louhichi

sums of independent random variables , Addison-Wesley Publishing Company (1954). MR 16,52d Limit distributions for sums of independent random variables

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# Strong laws of large numbers in von Neumann algebras

Acta Mathematica Hungarica
Author: Katarzyna Klimczak

J.  Funct.  Anal. 15 103 – 116 10.1016/0022-1236(74)90014-7 . [6] Petrov , V. V. 1972 Sums of Independent

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# Complete convergence for arrays

Periodica Mathematica Hungarica
Author: A. Gut

## Abstract

Let {(X nk, 1≤kn),n≥1}, be an array of rowwise independent random variables. We extend and generalize some recent results due to Hu, Mricz and Taylor concerning complete convergence, in the sense of Hsu and Robbins, of the sequence of rowwise arithmetic means.

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# Law of the iterated logarithm for self-normalized sums and their increments

Studia Scientiarum Mathematicarum Hungarica
Authors: Han-Ying Liang, Jong-Il Baek, and Josef Steinebach

425 445 Petrov, V. V., On the probabilties of large deviations for sums of independent random variables, Theory Probab. Appl , 10 (1965), 287

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# A law of the single logarithm for moving averages of random variables under exponential moment conditions

Studia Scientiarum Mathematicarum Hungarica
Author: H. Lanzinger

sums of independent random variables, Ann. Probab . 7 (1979), 745-789. MR 80i :60032 Large deviations of sums of independent random variables Ann. Probab

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# Limsup theorems and a uniform LIL for asymptotically negatively associated random sequences

Studia Scientiarum Mathematicarum Hungarica
Authors: Yong-Kab Choi and Kyo-Shin Hwang

1189 Petrov, V. V. , Sums of Independent Random Variables , Translated from the Russian by A. A. Brown, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82. Springer

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