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.

scholarly journals Approximations of Numerical Method for Neutral Stochastic Functional Differential Equations with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Differential Equations ◽  
Stochastic Systems ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Markovian Switching ◽  
Stochastic Functional Differential Equations ◽  
Em Method ◽  
Functional Differential ◽  
Stochastic Functional

Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama (EM) method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover, we obtain the convergence order of the approximate solutions.

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