On the Weak Law of Large Numbers of Randomly Indexed Partial Sums

  • Hong, Dug-Hun (Department of Statistics, Hysung Women's University, Kyungbuk 713-702) ;
  • Park, Suk-Young (Department of Statistics, Hysung Women's University, Kyungbuk 713-702) ;
  • Kim, Mal-Sook (Department of Statistics, Hysung Women's University, Kyungbuk 713-702)
  • Published : 1994.12.01

Abstract

The purpose of this note is to provide a general weak law of randomly indexed partial sums for arrays.

Keywords

References

  1. Real Analysis and Probability Ash,R.B.
  2. Sankhya Ser. v.A 51 Unifrom intergrability in the Cesaro sense and the weak law of large numbers Chandra,T.K.
  3. Annals of Mathematical Statistics v.40 An Lp-convergence theorem Chatterji,S.D.
  4. Annals of Mathematical Statistics v.42 On the Lp-convergence for $n^ {-1/p}S_n$, 0 < p < 2 Chow,Y.S.
  5. Probability Theory (2nd ed.) Chow,Y.S.;Teicher,H.
  6. The Annals of Probability v.2 On convergence in r-mean of some first passage times and randomly indexed partial sums Gut,A.
  7. Statistics and Probability Letters v.14 The weak law of large numbers arrays Gut,A.
  8. Mathematical Proceedings of the Cambridge Philosophical Society v.82 On the Lp-Convergence of sums of independent random variables Hall,P.
  9. Statistics and Probability Letters (to appear) On the weak law of large numbers for arrays Hong,D.H.;Oh,K.S.
  10. Annals of Mathematical Statistics v.39 On convergence in r-mean of normalized partial sums Pyke,R.;Root,D.
  11. The Annals of Probability v.9 A limit thorem for double arrays Rosalsky,A.;Teicher,H.