Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching

2016 ◽  
Vol 90 (8) ◽  
pp. 1703-1712 ◽  
Author(s):  
Quanxin Zhu
Keyword(s):  
Differential Equations ◽  
Markov Switching ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Lévy Noise ◽  
Stochastic Functional Differential Equations ◽  
Functional Differential ◽  
Levy Noise ◽  
Stochastic Functional

scholarly journals β -Stability in q -th Moment of Neutral Impulsive Stochastic Functional Differential Equations with Markovian Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Lassaad Mchiri ◽  
Mohamed Rhaima
Keyword(s):  
Differential Equations ◽  
Type Theorem ◽  
Functional Differential Equations ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Numerical Example ◽  
Lyapunov Techniques ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we investigate the β -stability in q-th moment for neutral impulsive stochastic functional differential equations with Markovian switching (NISFDEwMS). Moreover, β -stability in q-th moment is studied by using the Lyapunov techniques and a new Razumikhin-type theorem to prove our result. Finally, we check the main result by a numerical example.

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.

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