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COMPLETE CONVERGENCE FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM VARIABLES

  • Hu, Tien-Chung (Department of Mathematics Tsing Hua University) ;
  • Sung, Soo-Hak (Department of Applied Mathematics Pai Chai University) ;
  • Volodin, Andrei (Department of Mathematics and Statistics University of Regina)
  • Published : 2003.04.01

Abstract

Under some conditions on an array of rowwise independent random variables, Hu et at. (1998) obtained a complete convergence result for law of large numbers with rate {a$\_$n/, n $\geq$ 1} which is bounded away from zero. We investigate the general situation for rate {a$\_$n/, n $\geq$ 1) under similar conditions.

Keywords

References

  1. Commun. Statist. Theor. Meth. v.16 On sums of independent random vectors N.Etemadi https://doi.org/10.1080/03610928708829361
  2. An Introduction to Probability Theory and Its Applications Ⅰ,(3rd ed.) W.Feller
  3. Proceedings of the Fith Prague Symposium, Physica Verlag held September Complete convergence, Asmptotic Statistics, A.Gut
  4. Studies Math. v.52 Sums of independent Banach space valued random variables J. Hoffmann-JØrgensen https://doi.org/10.4064/sm-52-2-159-186
  5. Proc. Nat. Acad. Sci. v.33 Complete convergence and law of large numbers P.L.Hsu;H.Robbins https://doi.org/10.1073/pnas.33.2.25
  6. Statist. Probab. Lett. v.38 A note on complete convergence for arrays T.C.Hu.;D.Szynl;A.Rosalsky;A.I.Volodinr https://doi.org/10.1016/S0167-7152(98)00150-3
  7. Stochastic Analysis and Applications v.17 On complete convergence for arrays of rowwise independent random elements in Banach spaces T.C.Hu;D.Szynal;A.Rosalsky;A.L.Volodinr https://doi.org/10.1080/07362999908809645
  8. Statist. Probab. Lett. v.38;47 no.1 Addendum to A note on complete convergence for arrays T.C.Hu;A.L.Volodin
  9. Random Series and Stochostic Integralsc: Single and Multiple, S.Kwapiers;W.A.Woycznski
  10. Lecture Notes in Mathematics v.1206 Probabilistic methods in the geometry of Banach spaces G.Pisier https://doi.org/10.1007/BFb0076302

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  9. On Complete Convergence for Arrays of Dependent Random Variables vol.41, pp.9, 2012, https://doi.org/10.1080/03610926.2010.549282
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  16. On complete convergence for arrays of rowwise negatively associated random variables vol.52, pp.2, 2007, https://doi.org/10.4213/tvp183