scholarly journals Inequalities and exponential decay in time varying delay differential equations

2011 ◽  
Vol 54 (1-2) ◽  
pp. 794-802 ◽  
Author(s):  
Murat Adıvar ◽  
Youssef N. Raffoul
Keyword(s):  
Differential Equations ◽  
Exponential Decay ◽  
Delay Differential Equations ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Differential ◽  
Varying Delay

scholarly journals The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian Guo ◽  
Xueyin Tao
Keyword(s):  
Differential Equation ◽  
Numerical Experiments ◽  
Time Varying ◽  
Almost Sure Stability ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Time Varying Delay ◽  
Backward Euler ◽  
Delay Differential ◽  
Varying Delay

Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis.

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