Abstract Since stochastic differential equations (SDEs) driven by G -Brownian motion are of great importance in modeling situations that incorporate ambiguity, it is essential to address efficient numerical schemes to approximate the solution of such equations. The stream of research related to the numerical solutions of G -SDEs under standard assumptions is to some extent well understood. In this note, we are interested in designing an implicit theta θ -Euler–Maruyama scheme to approximate the solution of G -SDEs under locally Lipschitz continuous coefficients. The convergence of the proposed scheme is established using the stopping time technique. In addition, we investigate the exponentially/quasi-surely asymptotic stability property of the scheme.
Bahar Akhtari (Tue,) studied this question.