2018
Том 70
№ 8

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

Skorokhod A. V.

Abstract

Let $\xi_1, \xi_2,... \xi_n,...$ be independent identically distributed random variables, $s_{n0} = 0,\; s_{nk} = \cfrac1{\sqrt{n}}(\xi_1 + ... + \xi_k)$; and $\Phi_n(x_0, x_1, ..., x_r)$ the sequence of non-negative measurable functions for which $\lim_{n\rightarrow \infty}\sup_{x_0, x_1, ..., x_n}\Phi_n(x_0, x_1, ..., x_r) = 0$.
Limit theorems for random variables $\cfrac1n\sum_{k=0}^{n-r}\Phi_n(s_{nk},...,s_{nk+r})$ are obtained in the article.

Citation Example: Skorokhod A. V. Some limit theorems for additive functionals of a sequence of sums of independent random variables // Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 67-78.

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