Article
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The convergence and boundedness of solutions to SFDEs with the G-framework
Version 1
: Received: 22 August 2023 / Approved: 22 August 2023 / Online: 22 August 2023 (07:24:21 CEST)
A peer-reviewed article of this Preprint also exists.
Ullah, R.; Faizullah, F.; Zhu, Q. The Convergence and Boundedness of Solutions to SFDEs with the G-Framework. Mathematics 2024, 12, 279. Ullah, R.; Faizullah, F.; Zhu, Q. The Convergence and Boundedness of Solutions to SFDEs with the G-Framework. Mathematics 2024, 12, 279.
Abstract
Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space Cr((−∞,0];Rn). The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both LG2 and exponential estimates.
Keywords
G-Brownian motion; exponential and LG2 estimates; boundedness; Convergence
Subject
Physical Sciences, Other
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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