2026-04-19T16:10:05Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/5312882024-12-20T05:03:42Zcom_2072_199267com_2072_4427col_2072_201036

00925njm 22002777a 4500 dc Cima, A. author Gasull, A. author Mañosa, V. author 2021-03-19 Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the n dimensional case, the zero solution is globally asymptotically stable if and only if this stability index is n. Fixed n, let X be the random variable that assigns to each linear random dynamical system its stability index, and let pk with k = 0, 1, …, n, denote the probabilities that P(X = k). In this paper we obtain either the exact values pk, or their estimations by combining the Monte Carlo method with a least square approach that uses some affine relations among the values pk, k = 0, 1, …, n. The particular case of n-order homogeneous linear random differential or difference equations is also studied in detail. © 2021, University of Szeged. All rights reserved. http://hdl.handle.net/2072/531288 10.14232/ejqtde.2021.1.15 Stability index of linear random dynamical systems