The LpG(W)-continuity of solutions to neutral stochastic differential equations driven by G -Brownian motion
*Zakaria BoumezbeurCorresponding authorboumezbeurza@gmail.comDepartment of MathematicsUniversity of Badji-MokhtarAnnaba, 23000, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 15 Nov 2023
- Published Online:
- 31 May 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1998
- Pages:
- 2475–2489
Abstract
Keywords
Subject Classifications
References
[1] M. Abouagwa, J. Li, “G-neutral stochastic differential equations with variable delay and non-Lipschitz coefficients,” Discrete and Continuous Dynamical Systems-Series B, vol. 25, no. 4, pp. 1583-1606 (2020).
[2] F. Faizullah, A.A. Memom, M.A. Rana, M. Hanif, “The p-moment exponential estimates for neutral stochastic functional differential equations in the G-framework,” Journal of Computational Analysis and Applications, vol. 26, no. 1, pp. 81-90 (2019).
[3] X. He, S. Han, J. Tao, “Averaging principle for SDEs of neutral type driven by G-Brownian motion,” Stochastics and Dynamics, vol. 19, no. 1, pp. 22 (2019).
[4] V. Kolmanovskii, A. Myshkis, “Applied Theory of Functional Differential Equations,” Kluwer Academic Publishers, Norwell (1992).
[5] V. Kolmanovskii, V. Nosov, “Stability of Functional Differential Equations,” Academic Press, New York (1986).
[6] G. Liu, S. Peng, F. Wang, “On the exit times for SDEs driven by G-Brownian motion,” arXiv:1804.05610 (2018).
[7] Q. Lin, “Differentiability of stochastic differential equations driven by the G-Brownian motion,” Science China Mathematics, vol. 56, no. 5, pp. 1087-1107 (2013).
[8] X. Mao, “Stochastic differential equations and applications,” Elsevier Science (2007).
[9] Z. Min, J. Li, Y. Zhu, “Exponential stability of neutral stochastic functional differential equations driven by G-Brownian motion,” Journal of Nonlinear Science and Applications, vol. 10, pp. 1830-1841 (2017).
[10] S. Peng, “Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation,” Stochastic Processes and their Applications, vol. 118, no.12, pp. 2223- 2253 (2008).
[11] S. Peng, “ G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type,” Stochastic Analysis and Applications, vol. 2, pp. 541-567 (2007).
[12] S. Peng, “ G-Brownian motion and dynamic risk measure under volatility uncertainty,” arXiv:0711.2834 (2007).
[13] S. Reza Hejazi, N. Habibi, E. Dastranj, E. Lashkarian, “Numerical approximations for time-fractional Fokker-Planck-Kolmogorov equation of geometric Brownian motion,” Journal of Interdisciplinary Mathematics, vol. 23, no. 7, pp. 1387-1403 (2020).
[14] Y. Ren, X. Jia, L. Hu, “Exponential stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion,” Discrete and Continuous Dynamical Systems-Series B”, vol. 20, no. 7, pp. 2157-2169 (2015).
[15] Y. Xiao, L. Zhang, Y. Fang, “Numerical solution stability of general stochastic differential equation,” Journal of Interdisciplinary Mathematics, vol. 21, no. 6, pp. 1471-1479 (2018).
[16] D. Zhang, Z. Chen, “Exponential stability for stochastic differential equation driven by G-Brownian motion,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1906-1910 (2012).




