The Behavior of Sums of Independent Random Variables

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1975 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 19, pages 374-379 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Kruglov, V. M.;

doi: 10.1137/1119042

The Behavior of Sums of Independent Random Variables

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Abstract

werden ausgedehnt auf die Situation: \(\vert a_n^{-1}(S_n - \text{Med}(S_n))\vert\) bleibt mit \(P=1\) beschränkt \((a_n\to\infty\) geeignet), die als äquivalent zu \[ a_n^{-1} b_n^{-1} (S_n - \text{Med}(S_n)) \text{ konvergiert gegen Null mit }P=1 \] nachgewiesen wird \((b_n\to\infty\) geeignet).

Keywords

Strong limit theorems, Sums of independent random variables; random walks

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