Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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IDENTICALLY DISTRIBUTED UNCORRELATED RANDOM VARIABLES NOT FULFILLING THE WLLN

  • Landers, Dieter (UNIVERSITY OF COLOGNE, MATHEMATISCHES INSTITUT) ;
  • Rogge, Lothar (UNIVERSITY OF DUISBURG, GERHARD-MERCATOR-UNIVERSITAT DUISBURG)
  • Published : 2001.08.01
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Abstract

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.

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References

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