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

Author

Listed:
  • Rahman Ullah

    (School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China)

  • Faiz Faizullah

    (College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan)

  • Quanxin Zhu

    (MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China)

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 C r ( ( − ∞ , 0 ] ; R n ) . The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both L G 2 and exponential estimates.

Suggested Citation

  • Rahman Ullah & Faiz Faizullah & Quanxin Zhu, 2024. "The Convergence and Boundedness of Solutions to SFDEs with the G-Framework," Mathematics, MDPI, vol. 12(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:279-:d:1319395
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    References listed on IDEAS

    as
    1. Faiz Faizullah, 2014. "Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, September.
    2. Luo, Peng & Wang, Falei, 2015. "On the comparison theorem for multi-dimensional G-SDEs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 38-44.
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