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. Korolev
  • V. M. Kruglov
Article

DOI: 10.1007/BF02362284

Cite this article as:
Korolev, V.Y. & Kruglov, V.M. J Math Sci (1998) 89: 1495. doi:10.1007/BF02362284

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.

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