scholarly journals The split-step backward Euler method for linear stochastic delay differential equations

2009 ◽  
Vol 225 (2) ◽  
pp. 558-568 ◽  
Author(s):  
Haomin Zhang ◽  
Siqing Gan ◽  
Lin Hu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Euler Method ◽  
Backward Euler Method ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Delay Differential

scholarly journals Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Zhanhua Yu ◽  
Mingzhu Liu
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Euler Method ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Delay Differential ◽  
Theoretical Results

We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.

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