Non–linear functionals preserving normal distribution and their asymptotic normality

27.05.2019, 12:00  –  Golm, Haus 9, Raum 0.13
SFB-Seminar

Linda Khachatryan (Yerevan, Armenia)

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.