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.

scholarly journals Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Haiyan Yuan
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Euler Method ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Exponential Euler Method ◽  
The Stability ◽  
Delay Differential

This paper is concerned with the numerical solutions of semilinear stochastic delay differential equations driven by G-Brownian motion (G-SLSDDEs). The existence and uniqueness of exact solutions of G-SLSDDEs are studied by using some inequalities and the Picard iteration scheme first. Then the numerical approximation of exponential Euler method for G-SLSDDEs is constructed, and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent, and it can reproduce the stability of the analytical solution under some restrictions. Numerical experiments are presented to confirm the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document