Contents V.1, N.1, 2010

  • ON NONCLASSICAL LIMIT THEOREMS FOR SUMS OF INDEPENDENTRANDOM VARIABLES
    SHAKIR FORMANOV, ASKAR AKHMEDOV, LOLA SHARIPOVA (pp. 68-80)

    • Abstract.

    Nonclassical limit theorems, unlike classical ones, do not require satisfaction of theuniform limit smallness condition. In the nonclassical situation of summation of independentrandom variables, the class of limit distributions is extended maximally, and it coincides withthe set of all distributions.

    Keywords:

    central limit problem, Kolmogorov’s model in the theory of summation of ran-dom variables, uniform limit smallness condition, nonclassical central limit theorem, Stein-Tikhomirov’s method, characteristic function.

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