Finding a response matrix for a discrete linear dynamic stochastic system. (Russian, English) Zbl 1121.93346

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 5, 817-826 (2004); translation in Comput. Math. Math. Phys. 44, No. 5, 771-780 (2004).
An algorithm is presented that computes the response matrix to the external action of a discrete linear stochastic dynamical system. The well-know estimates for the norms of the powers of a matrix in terms of solutions to the discrete Lyapunov equation are used in justifying the algorithm. The results are shown to be applicable to stochastic dynamical systems with continuous time. Results of numerical experiments are provided.


93C55 Discrete-time control/observation systems
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
37H10 Generation, random and stochastic difference and differential equations
39A10 Additive difference equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)