Article

Journal of Mathematical Sciences

, Volume 89, Issue 5, pp 1495-1506

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

  • V. Yu. KorolevAffiliated withFaculty of Computational Mathematics and Cybernetics, Moscow State University
  • , V. M. KruglovAffiliated withFaculty of Computational Mathematics and Cybernetics, Moscow State University

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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.