Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE WEAK LAW FOR RANDOMLY INDEXED PARTIAL SUMS FOR ARRAYS

  • Hong, Dug-Hun (School of Mech. and Autom. Engin., Catholic University of Taegu) ;
  • Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University) ;
  • Andrei I.Volodin (Department of Mathematics and Stat., Regina University)
  • Published : 2001.04.01
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Abstract

For randomly indexed sums of the form (Equation. See Full-text), where {X(sub)ni, i$\geq$1, n$\geq$1} are random variables, {N(sub)n, n$\geq$1} are suitable conditional expectations and {b(sub)n, n$\geq$1} are positive constants, we establish a general weak law of large numbers. Our result improves that of Hong [3].

Keywords

References

  1. Probability Theory: Independence, Interchageability, Martingales(3rd ed.) Y. S. Chow;H. Teicher
  2. Statist. Probab. Lett. v.14 The weak law of large numbers for arrays A. Gut
  3. Statist. Probab. Lett. v.28 On the weak law of large numbers for randomly indexed partial sums for arrays D. H. Hong
  4. Statist. Probab. Lett. v.22 On the weak law of large numbers for arrays D. H. Hong;K. S. Oh
  5. On the weak law of large numbers for randomly indexed partial sums for arrays P. Kowalski and Z. Rychlik
  6. Statist. Probab. Lett. v.38 Weak law of large numbers for arrays S. H. Sung