We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions of G-SFDEs are given. We show that the unique solution of G-SFDEs gets convergence from Cauchy-Maruyama (CM) approximate solutions. The existence theorem for G-SFDEs is developed with the above mentioned scheme.
"Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme." Abstr. Appl. Anal. 2014 (SI51) 1 - 8, 2014. https://doi.org/10.1155/2014/809431