Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching

Junhao Hu and Zhiying Xu

Mathematical Problems in Engineering, 2014, vol. 2014, 1-15

Abstract:

We develop exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching modeled by a continuous-time Markov chain which has a large state space. To overcome the computational effort and the complexity, we split the large-scale system into several classes and lump the states in each class into one class by the different states of changes of the subsystems; then, we give a limit system to effectively “replace” the large-scale system. Under suitable conditions, using the stability of the limit system as a bridge, the desired asymptotic properties of the large-scale system with Brownian motion and Poisson jump are obtained by utilizing perturbed Lyapunov function methods and Razumikhin-type criteria. Two examples are provided to demonstrate our results.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:907982

DOI: 10.1155/2014/907982

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