2019
Том 71
№ 2

All Issues

Stepakhno V. I.

Articles: 4
Brief Communications (Russian)

On samples of independent random vectors in spaces of infinitely increasing dimension

Ruzhilo M. Ya, Stepakhno V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1706–1711

We study the asymptotic behavior of a set of random vectors ξi, i = 1,..., m, whose coordinates are independent and identically distributed in a space of infinitely increasing dimension. We investigate the asymptotics of the distribution of the random vectors, the consistency of the sets M m (n) = ξ1,..., ξm and X n λ = x ∈ X n: ρ(x) ≤ λn, and the mutual location of pairs of vectors.

Article (Ukrainian)

Empirical correlation operator and many-dimensional Hermite polynomials

Stepakhno V. I.

↓ Abstract

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 871–875

The action of an empirical correlation operator on the subspaces of vector Hermite polynomials of a given order is studied. The principal part of this operator is selected.

Article (Ukrainian)

Large samples of observations of random vectors of large dimension

Stepakhno V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1413–1418

Article (Ukrainian)

A central limit theorem for Hermitian polynomials of independent Gaussian variables

Skorokhod A. V., Stepakhno V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1681–1686