scholarly journals MEAN SQUARE EXPONENTIAL DISSIPATIVITY OF SINGULARLY PERTURBED STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 29 (1) ◽  
pp. 205-212 ◽  
Author(s):  
Liguang Xu ◽  
Zhixia Ma ◽  
Hongxiao Hu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Singularly Perturbed ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Delay Differential

scholarly journals Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Peiguang Wang ◽  
Yan Xu
Keyword(s):  
Differential Equations ◽  
Operator Theory ◽  
Delay Differential Equations ◽  
Averaging Principle ◽  
Neutral System ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Delay Term ◽  
Delay Differential

In this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition. By using the linear operator theory, we deal with the difficulty brought by delay term of the neutral system and obtain the conclusion that the solutions of neutral stochastic delay differential equations with impulses converge to the solutions of the corresponding averaged stochastic delay differential equations without impulses in the sense of mean square and in probability. At last, an example is presented to show the validity of the proposed theories.

scholarly journals Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiyong Li ◽  
Siqing Gan
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Analytical And Numerical Solutions ◽  
Mean Square Stability ◽  
Delay Differential

This paper is concerned with the stability of analytical and numerical solutions fornonlinearstochastic delay differential equations (SDDEs) with jumps. A sufficient condition for mean-square exponential stability of the exact solution is derived. Then, mean-square stability of the numerical solution is investigated. It is shown that the compensated stochastic θ methods inherit stability property of the exact solution. More precisely, the methods are mean-square stable for any stepsizeΔt=τ/mwhen1/2≤θ≤1, and they are exponentially mean-square stable if the stepsizeΔt∈(0,Δt0)when0≤θ<1. Finally, some numerical experiments are given to illustrate the theoretical results.

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