Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

WEAK LAWS FOR WEIGHTED SUMS OF RANDOM VARIABLES

  • Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University)
  • Published : 2004.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

Keywords

References

  1. Sankhya, Ser. A v.51 no.3 Uniform integrability in the Cesaro sense and the weak law of large numbers T.K.Chandra
  2. Statist. Probab. Lett. v.14 no.1 The weak law of large numbers for arrays A.Gut https://doi.org/10.1016/0167-7152(92)90209-N
  3. Bull. Inst. Math. Acad. Sinica v.24 no.3 A general weak law of large numbers for arrays D.H.Hong;S.Lee
  4. Statist. Probab. Lett. v.22 no.1 On the weak law of large numbers for arrays D.H.Hong;K.S.Oh https://doi.org/10.1016/0167-7152(94)00047-C
  5. Collect. Math. v.45 no.2 Convergence of weighted sums of random variables and uniform integrability concerning the weights M.Ordonez Cabrera
  6. J. Math. Mech. v.15 Summability of independent random variables W.E.Pruitt
  7. Proc. Cambridge Philos. Soc. v.69 Convergence of weighted sums of independent random variables V.K.Rohatgi https://doi.org/10.1017/S0305004100046685
  8. Statist. Probab. Lett. v.38 no.2 Weak law of large numbers for arrays S.H.Sung https://doi.org/10.1016/S0167-7152(97)00159-4
  9. Statist. Probab. Lett. v.42 no.3 Weak law of large numbers for arrays of random variables S.H.Sung https://doi.org/10.1016/S0167-7152(98)00219-3
  10. Internat. J. Math. Math. Sci. v.8 no.4 A note on convergence of weighted sums of random variables X.C.Wang;M.B.Rao https://doi.org/10.1155/S0161171285000898

Cited by

  1. Strong laws of large numbers and mean convergence theorems for randomly weighted sums of arrays under a condition of integrability vol.9, pp.5, 2012, https://doi.org/10.1016/j.stamet.2012.02.003
  2. Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables vol.377, pp.2, 2011, https://doi.org/10.1016/j.jmaa.2010.11.042