Armenian Journal of Mathematics

Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality

Khachatryan, L. A. and Nahapetian, B. S. (2018) Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality. Armenian Journal of Mathematics, 10 (5). pp. 1-20. ISSN 1829-1163

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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 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.

Item Type:Article
Subjects:26-xx Real functions
46-xx Functional analysis
60-xx Probability theory and stochastic processes
ID Code:827
Deposited By:Professor Anry Nersesyan
Deposited On:02 Jul 2018 11:51
Last Modified:02 Jul 2018 11:55

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