Asymptotic behavior of a class of stochastic semigroups in the Bernoulli scheme - Chani, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
The family of subalgebras that describe the space of complex-valued $2 × 2$ matrices is selected. In this space, the stochastic semigroup $Y_n = X_n X_{n-1} ... X_1, \; n = \overline{1, ∞}$, is considered, where $\{X_ , і = \overline{1, ∞}\}$ 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.