Details

Autor(en) / Beteiligte

• Landers, Dieter
• Rogge, Lothar

Titel

IDENTICALLY DISTRIBUTED UNCORRELATED RANDOM VARIABLES NOT FULFILLING THE WLLN

Ist Teil von

• Taehan Suhakhoe hoebo, 2001, Vol.38 (3), p.605-610

Erscheinungsjahr

2001

Link zum Volltext

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• It is shown that for each 1 < p < 2 there exist identically distributed uncorrelated random variables $X_n\; with\;E({$\mid$X_1$\mid$}^p)\;<\;{\infty}$, not fulfilling the weak law of large numbers (WLLN). If, however, the random variables are moreover non-negative, the weaker integrability condition $E(X_1\;log\;X_1)\;<\;{\infty}$ already guarantees the strong law of large numbers.