Consider a stochastic differential delay equation driven by G-Brownian motion (G-SDDE) dx(t) = f(x(t), x(t − τ))dt + g(x(t), x(t − τ))dB(t) + h(x(t), x(t − τ))dhBi(t). Under the global Lipschitz condition for the G-SDDE, we show that the G-SDDE is exponentially stable in mean square if and only if for sufficiently small step size, the Euler-Maruyama (EM) method is exponentially stable in mean square. Thus, we can carry out careful numerical simulations to investigate the exponential stability of the underlying G-SDDE in practice, in the absence of an appropriate Lyapunov function. A numerical example is provided to illustrate our results.
|Journal||Applied Mathematics Letters|
|Publication status||Accepted/In press - 23 Apr 2019|
- mean square stability
- EM method
- stability equivalence
- G-Brownian motion
- Euler-Maruyama method
- stochastic differential delay equations
Deng, S., Fei, C., Fei, W., & Mao, X. (Accepted/In press). Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method. Applied Mathematics Letters.