### Abstract

Language | English |
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Journal | Applied Mathematics Letters |

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

### Fingerprint

### Keywords

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

### Cite this

*Applied Mathematics Letters*.

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**Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method.** / Deng, Shounian; Fei, Chen; Fei, Weiyin; Mao, Xuerong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method

AU - Deng, Shounian

AU - Fei, Chen

AU - Fei, Weiyin

AU - Mao, Xuerong

PY - 2019/4/23

Y1 - 2019/4/23

N2 - 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.

AB - 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.

KW - mean square stability

KW - G-SDDE

KW - EM method

KW - stability equivalence

KW - G-Simulation

KW - G-Brownian motion

KW - Euler-Maruyama method

KW - stochastic differential delay equations

M3 - Article

JO - Applied Mathematics Letters

T2 - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -