2019
Том 71
№ 11

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

Chani A. S.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 11, pp 1779-1784.

Citation Example: Chani A. S. Asymptotic behavior of a class of stochastic semigroups in the Bernoulli scheme // Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1580–1584.

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