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

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  • Junhao Hu
  • Zhiying Xu

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.

Suggested Citation

  • Junhao Hu & Zhiying Xu, 2014. "Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-15, March.
    • Handle: RePEc:hin:jnlmpe:907982
    DOI: 10.1155/2014/907982
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