### Abstract

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.

Original language | English |
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Journal | Applied Mathematics Letters |

Publication status | Accepted/In press - 23 Apr 2019 |

### Keywords

- mean square stability
- G-SDDE
- EM method
- stability equivalence
- G-Simulation
- G-Brownian motion
- Euler-Maruyama method
- stochastic differential delay equations

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## Cite this

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*.