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Exponential Stability of Neutral Stochastic Functional Differential Equations with Two-Time-Scale Markovian Switching
- Source :
- Mathematical Problems in Engineering, Vol 2014 (2014)
- Publication Year :
- 2014
- Publisher :
- Hindawi Publishing Corporation, 2014.
-
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.
- Subjects :
- Lyapunov function
Markov chain
Article Subject
Differential equation
lcsh:Mathematics
General Mathematics
Mathematical analysis
General Engineering
lcsh:QA1-939
Stability (probability)
symbols.namesake
Exponential stability
lcsh:TA1-2040
symbols
State space
Applied mathematics
Limit (mathematics)
lcsh:Engineering (General). Civil engineering (General)
Brownian motion
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 1024123X
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....1c771d0894b5774f01dac8511caabb91
- Full Text :
- https://doi.org/10.1155/2014/907982