CALCULATING THE LYAPUNOV EXPONENT FOR GENERALIZED LINEAR SYSTEMS WITH EXPONENTIALLY DISTRIBUTED ELEMENTS OF THE TRANSITION MATRIX
Krivulin N.K. Evaluation of the Lyapunov exponent for generalized linear systems with the exponential distribution of elements of a transition matrix // Vestnik St.Petersburg University. Ser. 1. 2009. Issue 2. P. 37-47. A second-order generalized linear stochastic dynamical system is considered. The evolution of the system is described through a dynamical equation with a random transition matrix, which is linear in idempotent algebra with the operations of taking maximum and addition. It is assumed that some entries of the transition matrix are equal to zero, whereas the other entries are independent and exponentially distributed. The problem of evaluation of the Lyapunov exponent defined as the mean asymptotic growth rate of the system state vector is considered. The known results for the problem are restricted to the system with a matrix which has zero entries on its diagonal. In order to evaluate the Lyapunov exponent for the case of matrices which can have a zero row, zero diagonal entries, or only one zero entry, an approach is applied based on construction and analysis of a sequence of one-dimensional distribution functions. The Lyapunov exponent is evaluated as the mean value of the random variable determined by the limit distribution of the sequence. Bibliogr. 9 references.