Հտ․ 10 No. 5 (2018): Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

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  Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

  Linda Kachatryan, Boris Nahapetian

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  We introduce sufficiently wide classes of non--linear functionals preserving normal (Gaussian) distribution and establish various conditions under which a sequence of such functionals is asymptotically normal. As one of a consequence we obtain a generalization and sharpening of known results on the central limit theorem for weighted sums (linear functionals) of independent random variables.

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