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( Zakaria Boumezbeur ),( Hacène Boutabia ) 호남수학회 2023 호남수학학술지 Vol.45 No.3
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<sup>n</sup>) of bounded continuous R<sup>n</sup>-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space L<sub>BC</sub> (R<sup>n</sup>) of linear bounded operators from BC ([-r, 0] ;R<sup>n</sup>) to R<sup>n</sup>. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.