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

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 mart...

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Published inJournal of Taibah University for Science Vol. 13; no. 1; pp. 20 - 26
Main Authors Faizullah, Faiz, Khan, Ilyas, Salah, Mukhtar M., Alhussain, Ziyad Ali
Format Journal Article
LanguageEnglish
Published Taylor & Francis 11.12.2019
Taylor & Francis Group
Subjects
bounded solutions
differential equation
estimates
G-Brownian motion
non-linear growth and non-Lipschitz conditions
solutions
stochastic differential equations
universities
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Summary: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 . In view of non-linear growth and non-uniform Lipschitz conditions, we give estimates for the difference between the exact solution and approximate solutions of SDEs in the framework of G-Brownian motion.
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ISSN:1658-3655
1658-3655
DOI:10.1080/16583655.2018.1519884