Honam Mathematical Journal (호남수학학술지)

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

  • Zakaria Boumezbeur (Department of Mathematics, Faculty of Science, LaPS Laboratory, Badji Mokhtar University) ;
  • Hacene Boutabia (Department of Mathematics, Faculty of Science, LaPS Laboratory, Badji Mokhtar University)
  • Received : 2022.09.14
  • Accepted : 2023.02.09
  • Published : 2023.09.14
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Abstract

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] ; ℝn) of bounded continuous ℝn-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛BC (ℝn) of linear bounded operators from BC ([-r, 0] ; ℝn) to ℝn. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

Keywords

Acknowledgement

The authors acknowledge and deeply appreciate the careful reading and useful suggestions of the anonymous reviewers, which has improved the quality of this paper.

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