Evaluation of the Lyapunov exponent for generalized linear second-order exponential systems

Abstract

We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of new results on evaluation of asymptotic growth rate of the system state vector, which is called the Lyapunov exponent of the system.