Computation of the Lyapunov exponent of a generalized linear stochastic dynamical system with a second-order matrix

A stochastic dynamical system is considered, in which the state evolution is described by a generalized linear vector equation with a random transition matrix of the second order. The matrix entries include a random variable with exponential probability distribution, two positive constants, and zero. The mean asymptotic growth rate of state vector (the Lyapunov exponent) for the system is investigated. Evaluation of the Lyapunov exponent involves the development and analysis of convergence of series of one-dimensional distribution functions for all possible relations between the constants. The Lyapunov exponent is obtained as the mean value of the limiting distribution of a series. Bibliogr. 9.