Euler–Maruyama Schemes for G-Stochastic Volterra Equations

Abstract

We study Euler–Maruyama approximations for stochastic Volterra integral equations driven by G-Brownian motion. The proposed explicit Volterra scheme discretizes the drift term, the quadratic variation term and the stochastic integral term. Under standard Lipschitz, growth and time-regularity assumptions, we prove uniform moment bounds and strong mean-square convergence under sublinear expectation. The convergence rate reflects the time regularity of the Volterra kernels and recovers the classical order one–half in the root mean square sense in the Lipschitz case. A numerical experiment under volatility uncertainty illustrates the theory.