Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework

Autor: Faiz Faizullah, Ilyas Khan, Mukhtar M. Salah, Ziyad Ali Alhussain
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Journal of Taibah University for Science, Vol 13, Iss 1, Pp 20-26 (2019)
Druh dokumentu: article
ISSN: 1658-3655
16583655
DOI: 10.1080/16583655.2018.1519884
Popis: This article investigates the Euler-Maruyama approximation procedure for stochastic differential equations in the framework of G-Browinian motion with non-linear growth and non-Lipschitz conditions. The results are derived by using the Burkholder-Davis-Gundy (in short BDG), Hölder's, Doobs martingale's and Gronwall's inequalities. Subject to non-linear growth condition, it is revealed that the Euler-Maruyama approximate solutions are bounded in $ M_G^2([t_0,T];\mathbb {R}^n) $ . In view of non-linear growth and non-uniform Lipschitz conditions, we give estimates for the difference between the exact solution $ Z(t) $ and approximate solutions $ Z^q(t) $ of SDEs in the framework of G-Brownian motion.
Databáze: Directory of Open Access Journals
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