Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Authors

  • Linda Kachatryan Institute of Mathematics, NAS
  • Boris S. Nahapetian Institute of Mathematics, NAS

DOI:

https://doi.org/10.52737/18291163-2018.10.5-1-20

Keywords:

normal distribution, central limit theorem, non-linear functional on several variables

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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Published

2018-06-19 — Updated on 2022-10-02

Versions

Issue

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

Section

Articles

License

Copyright (c) 2018 Armenian Journal of Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
L. Kachatryan and B. Nahapetian, “Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality”, Armen.J.Math., vol. 10, no. 5, pp. 1–20, Oct. 2022, doi: 10.52737/18291163-2018.10.5-1-20.