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A Note on pth Moment Estimates for Stochastic Functional Differential Equations in the Framework of G-Brownian Motion

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Abstract

This paper presents the study of path-wise and moment estimates for the solutions to stochastic functional differential equations in the framework of G-Brownian motion. Under the linear growth condition, the pth moment estimates for the solutions to GSFDEs are investigated. The properties of G-expectations, Hölder’s inequality, Bihari’s inequality, Gronwall’s inequality and Burkholder–Davis–Gundy (BDG) inequalities are used to develop the theory of pth moment estimates. In addition, the continuity of pth moment and path-wise asymptotic estimates for the solutions to GSFDEs are shown.

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Acknowledgments

The author acknowledges and deeply appreciates the careful reading and useful suggestions of the antonymous reviewer, which has improved the quality of this paper.

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Authors and Affiliations

  1. Department of BS&H, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Faiz Faizullah

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  1. Faiz Faizullah
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Correspondence to Faiz Faizullah.

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Faizullah, F. A Note on pth Moment Estimates for Stochastic Functional Differential Equations in the Framework of G-Brownian Motion. Iran J Sci Technol Trans Sci 41, 1131–1138 (2017). https://doi.org/10.1007/s40995-016-0067-y

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  • DOI: https://doi.org/10.1007/s40995-016-0067-y

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