Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality (Armenian Journal of Mathematics, 2018)
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.
Keywords: normal distribution; central limit theorem; non-linear functional on several variables