2019
Том 71
№ 8

# Slobodenyuk N. P.

Articles: 3
Article (Ukrainian)

### Asymptotic decomposition of the distribution of the number of recurrences of a random walk in the initial state

Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 58—65

Article (Russian)

### Limiting distributions for additive functionals of a sequence of sums of independent equally distributed lattice random variables

Ukr. Mat. Zh. - 1965. - 17, № 2. - pp. 97-105

Article (Russian)

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

Ukr. Mat. Zh. - 1964. - 16, № 1. - pp. 41-60

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.