scholarly journals Razumikhin-type theorems on moment exponential stability of functional differential equations involving two-time-scale Markovian switching

2015 ◽  
Vol 5 (3) ◽  
pp. 697-719 ◽  
Author(s):  
Fuke Wu ◽  
◽  
George Yin ◽  
Le Yi Wang ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Time Scale ◽  
Functional Differential Equations ◽  
Markovian Switching ◽  
Functional Differential ◽  
Moment Exponential Stability

scholarly journals Razumikhin-type theorem on time-changed stochastic functional differential equations with Markovian switching

2019 ◽  
Vol 17 (1) ◽  
pp. 689-699 ◽  
Author(s):  
Xiaozhi Zhang ◽  
Chenggui Yuan
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Razumikhin Theorem ◽  
Functional Differential ◽  
Stability Results ◽  
Stochastic Functional

Abstract This work is mainly concerned with the exponential stability of time-changed stochastic functional differential equations with Markovian switching. By expanding the time-changed Itô formula and the Razumikhin theorem, we obtain the exponential stability results for the time-changed stochastic functional differential equations with Markovian switching. What’s more, we get many useful stability results by applying our new results to several important types of functional differential equations. Finally, an example is given to demonstrate the effectiveness of the main results.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Junhao Hu ◽  
Zhiying Xu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Time Scale ◽  
Large Scale ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Limit System ◽  
Large Scale System ◽  
Functional Differential ◽  
Stochastic Functional

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.

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