Search Results

You are looking at 1 - 10 of 12 items for :

  • "sums of independent random variables" x
  • All content x
Clear All

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

Restricted access

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

Restricted access

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).
Restricted access

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

Restricted access

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

Restricted access

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.

Restricted access

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

Restricted access

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

Restricted access

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

Restricted access