Journal of Mathematical Sciences

, Volume 89, Issue 5, pp 1495–1506 | Cite as

A criterion of convergence of nonrandomly centered random sums of independent identically distributed random variables

  • V. Yu. Korolev
  • V. M. Kruglov

Abstract

Necessary and sufficient conditions are presented for the weak convergence of random sums of independent identically distributed random variables in the double array scheme. As corollaries, two criteria of the normal convergence of random sums are given.

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. Yu. Korolev
    • 1
  • V. M. Kruglov
    • 1
  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

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