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OALib Journal期刊
ISSN: 2333-9721
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-  2019 

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

DOI: https://doi.org/10.1080/16583655.2018.1519884

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Abstract:

ABSTRACT 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), H?lder'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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