Armenian Journal of Mathematics, 10(6)
2022; 1–20
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Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Linda Kachatryan*, Boris Nahapetian

Received: 2024-12-17 · Published: 2022-10-02

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality
Authors
Linda Kachatryan, Boris Nahapetian
Source journal
Armenian Journal of Mathematics, 10(6)
Published
2022-10-02
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2018.10.5-1-20

Abstract

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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