DIFFERENTIABILITY OF NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G-BROWNIAN MOTION WITH RESPECT TO THE INITIAL DATA

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ;R n ) of bounded continuous R n -valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space L BC (R n ) of linear bounded operators from BC ([-r, 0] ;R n ) to R n . We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.