2019
Том 71
№ 11

# Chani A. S.

Articles: 2
Article (Russian)

### Asymptotic behavior of a class of stochastic semigroups in the Bernoulli scheme

Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1580–1584

The family of subalgebras that describe the space of complex-valued $2 \times 2$ matrices is selected. In this space, the stochastic semigroup $Y_n = X_n X_{n-1} ... X_1, \; n = \overline{1, \infty}$, is considered, where $\{X_ , і = \overline{1, \infty}\}$ are independent equally distributed random matrices taking two values. For the stochastic semigroup $Y_n$, whose phase space belongs to one of the subalgebras, the index of exponential growth is calculated explicitly.

Article (Russian)

### Asymptotic behavior of the products of random matrices with values on a solvable Lie algebra

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 1045–1048

The index of exponential growth is found for the products of random matrices with values on a solvable Lie algebra. The result is expressed via the eigenvalues of the terms.