Асимптотическое поведение одного класса стохастических полугрупп в схеме Бернулли

Abstract

The family of subalgebras that describe the space of complex-valued 2×2 matrices is selected. In this space, the stochastic semigroup Yn=XnXn−1...X1, n = 1,∞, is considered, where {Xi, і = 1,∞} are independent equally distributed random matrices taking two values. For the stochastic semigroup Yn, whose phase space belongs to one of the subalgebras, the index of exponential growth is calculated explicitly.