Abstract
In Chap. 7 sufficient conditions for the asymptotic mean-square stability of the solutions of stochastic differential equations with delay and Markovian switching are obtained. Different ways of constructing Lyapunov functionals for getting stability conditions are considered. Taking into account that it is difficult enough in each case to get analytical stability conditions, a numerical procedure for investigation of the stability of stochastic systems with Markovian switching is considered here. This procedure can be used in the cases where analytical conditions of stability are absent. In particular, an application to Markov chain with two states and numerical simulation of systems with Markovian switching are considered. Some examples of using the proposed numerical procedure are considered. The results of the calculations are presented by 15 figures.
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Shaikhet, L. (2013). Stochastic Systems with Markovian Switching. In: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00101-2_7
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DOI: https://doi.org/10.1007/978-3-319-00101-2_7
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00100-5
Online ISBN: 978-3-319-00101-2
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