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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Mathematics
, 2025, Issue 1, pp. 1–10
ISSN Online: 0000-0000
DOI:
10.xxxx/example-doi