2017
Том 69
№ 6

# Some limit theorems for additive functionals of a sequence of sums of independent random variables

Slobodenyuk N. P.

Abstract

Let $\xi_1, \xi_2, ...,\xi_n,...$ be independent identically distributed random variables, $S_{n0} = 0,\; S_{nk} = \frac1{\sqrt{n}} (\xi_1 + ...+ \xi_k)$, and $f_n(x, у)$ the sequence of measurable functions for which $\lim_{n\rightarrow \infty } \sup_{x, y} |f_n(x, у)| \rightarrow 0$. Limit theorems for random variables $\sum_{k=0}^{n—1}f_n(S_{nk}, S_{nk+1})$ are obtained.

Citation Example: Slobodenyuk N. P. Some limit theorems for additive functionals of a sequence of sums of independent random variables // Ukr. Mat. Zh. - 1964. - 16, № 1. - pp. 41-60.

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