On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework

Faiz Faizullah

doi:10.1186/s40064-016-2388-x

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework

Springerplus. 2016 Jun 24;5(1):872. doi: 10.1186/s40064-016-2388-x. eCollection 2016.

Author

Faiz Faizullah¹

Affiliation

¹ Department of Basic Sciences and Humanities, College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan.

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.

Keywords: G-Brownian motion; Non-linear growth condition; Path-wise asymptotic estimates; Stochastic functional differential equations; pth Moment estimates.