Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme

الملخص EN

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 X k 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.