Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지

SLIN FOR WEIGHTED SUMS OF STOCHASTICALLY DOMINATED PAIRWISE INDEPENDENT RANDOM VARIABLES

  • Sung, Soo-Hak (Department of Applied Mathematics, Paichai University)
  • Published : 1998.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

Keywords

References

  1. Stochastic Anal. Appl. v.5 Some general strong laws for weighted sums of stochastically dominated random variables A. Adler;A. Rosalsky
  2. Bull. Inst. Math. Acad. Sinica v.17 On the Chow-Robbins fair games problems A. Adler;A. Rosalsky
  3. Bull. Inst. Math. Acad. Sinica v.20 Some strony laws of large numbers for sums of random elements A. Adler;A. Rosalsky;R. L. Taylor
  4. Interchangeability, Martingales(2nd ed.) Probability Theory: Independence Y. S. Chow;H. Teicher
  5. Amer. J. Math. v.68 A limiting theorem for random variables with infinite moments W. Feller
  6. Stochastic Process. Appl. v.26 A strong law for a set-indexed partical sum process with applications to exchangeable and stationary sequences A. Rosalsky