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 = 1, ∞, is considered, where {X_ , і = 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.