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 |
|---|---|
| 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
Fingerprint Dive into the research topics of 'Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method'. Together they form a unique fingerprint.
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.