The Convergence and Boundedness of Solutions to SFDEs with the G-Framework

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
• L G 2 estimates%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> exponential and <named-content content-type="inline-formula"><inline-formula> <mml:math display="block" id="mm300"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi mathvariant="double-struck">L</mml:mi> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> estimates
• boundedness
• convergence