Journal of Mathematical Sciences

, Volume 91, Issue 3, pp 3002–3004 | Cite as

The central limit theorem without the condition of independence

  • L. Szeidl
  • V. M. Zolotarev


Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions. and mean metric of order q.


Characteristic Function Limit Theorem Random Vector Central Limit Theorem Independent Random Variable 
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  1. 1.
    Yu. V. Prokhorov, “Local limit theorems for sums of independent summands,”Usp. Mat. Nauk,7, No. 3(49). 112–125 (1952).Google Scholar
  2. 2.
    V. M. Kruglov, “A global limit theorem for the sums of independent random variables,”Dokl. Akad. Nauk SSSR. 219, 542–545 (1974).MATHMathSciNetGoogle Scholar
  3. 3.
    V. M. Zolotarev, “On the measure of dependence of random varables,”Teor. Veroyatn. Primen.,36, 854–857 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • L. Szeidl
    • 1
  • V. M. Zolotarev
    • 2
  1. 1.Eötvös Loránd UniversityBudapestHungary
  2. 2.Steklor Mathematical InstituteMoscowRussia

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