Publication Details:
Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
Non-linear Functionals Preserving Normal Distribution and Their Asymptotic Normality
Creator:
L. A. Khachatryan ; B. S. Nahapetian
Contributor(s):
Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
Subject:
Mathematics ; Functional analysis ; Probability theory and stochastic processes
Coverage:
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.
Publisher:
National Academy of Sciences of Armenia
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia
Digitization:
ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան