title: On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.
abstract: The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.
authors.affiliation: Department of Basic Sciences and Humanities, College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan.
authors.forename: Faiz
authors.initials: F
authors.lastname: Faizullah
keywords: G-Brownian motion; Non-linear growth condition; Path-wise asymptotic estimates; Stochastic functional differential equations; pth Moment estimates