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WEAK LAWS FOR WEIGHTED SUMS OF RANDOM VARIABLES

  • Sung, Soo-Hak (Department of Applied Mathematics, Pai Chai University)
  • Published : 2004.05.01

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.

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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