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

A family of subalgebras describing the space of complex-valued 2×2 matrices is selected. In this space, a stochastic semigroupY_n=X_nX_–1 ...X₁,n=, is considered, where {X_i, i=} are independent equally distributed random matrices taking two values. For a stochastic semigroupY_n, whose phase space belongs to one of the subalgebras, the index of exponential growth is determined explicitly.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1580–1584, November, 1993.