loading page

Convergence and asymptotical stability of numerical solutions for semi-linear stochastic delay differential equations driven by G-Brownian motion
  • Haiyan Yuan
Haiyan Yuan
Heilongjiang Institute of Technology

Corresponding Author:[email protected]

Author Profile

Abstract

There are few numerical analysis results for semi-linear stochastic delay dif- ferential equations driven by G-Brownian motion(G-SLSDDEs). This paper is concerned with the numerical solutions of the G-SLSDDEs to fill this gap. In this paper, existence and uniqueness of exact solutions of semi-linear stochastic delay differential equations driven by G-Brownian motion are studied first, some suitable conditions for the mean-square stability of the exact solution are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay differential equations driven by G-Brownian motion is constructed, the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with the strong order 1/2 and the exponential Euler method can reproduce the mean- square exponential stability of the analytical solution under some restrictions on the step size. Finally, numerical experiments are presented to confirm the theoretical results.