Have a personal or library account? Click to login
Existence Result for a Stochastic Functional Differential System Driven by G-Brownian Motion with Infinite Delay Cover

Existence Result for a Stochastic Functional Differential System Driven by G-Brownian Motion with Infinite Delay

Open Access
|Apr 2024

References

  1. BAO, H.—JIANG, D.: Existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp (Ω,Ch), Stoch. Dyn. 9 (2009), no. 4, 597–612. DOI:10.1142/s0219493709002786.
  2. FAIZULLAH, F.: Existence and uniqueness of solutions to SFDEs driven by G-Brownian motion with non-Lipschitz conditions, J. Comput. Anal. Appl. 23 (2017), no. 2, 344–354.
  3. FAIZULLAH, F.—REHMAN, M.U.—SHAHZAD, M.—CHOHAN, I.: On existence and comparison results for solutions to stochastic functional differential equations in the G-framework, J. Comput. Anal. Appl. 23 (2017), 693–702.
  4. KOLÁŘOVÁ, E.: Applications of second order stochastic integral equations to electrical networks, Tatra Mt. Math. Publ. 63 (2015), 163–173.
  5. KOLÁŘOVÁ, E.—BRANĆIK, L.: Stochastic Differential Equations Describing Systems with Coloured Noise, Tatra Mt. Math. Publ. 71 (2018), 107–99.
  6. PENG, S.: Nonlinear Expectations and Stochastic Calculus under Uncertainty, Probability Theory and Stochastic Modelling, Springer-Verlag, Berlin, Heidelberg, 2019. DOI: 10.1007/978-3-662-59903-7
  7. PENG, S.: Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations, Sci. China Ser. A-Math. 52 (2009), 1391–1411.
  8. PENG, S.: Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stochastic Process. Appl. 118 (2008), no. 12, 2223–2253.
  9. PENG, S.: G-expectation, G-Brownian motion and related stochastic calculus of Itô’s type. In: (Benth et al., eds.) Stochastic Analysis and Applications: The Abel Symposium 2005. Springer-Verlag, Berlin, Heidelberg, 2007, pp. 541–567.
  10. REN, Y.—BI, Q—SAKTHIVEL, R.: Stochastic functional differential equations with infinite delay driven by G-Brownian motion, Math. Methods Appl. Sci. 36 (2013), no. 13, 1746–1759.
  11. REN, Y.—XIA, N.: Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 210 (2009), no. 1, 72–79.
  12. REN, Y.—LU, S.—XIA, N.: Remarks on the existence and uniqueness of the solution to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. 220 (2008), no. 1, 364–372.
  13. WANG, Y.—WU, F.—MAO, X.—ZHU, E.: Advances in the LaSalle-type theorems for stochastic functional differential equations with infinite delay, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), no. 1, 287–300.
  14. WEI, F.—WANG, K.: The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl. 331 (2007), no. 1, 516–531.
  15. WU, F.—YIN, G.—MEI, H.: Stochastic functional differential equations with infinite delay, J. Differential Equations 262 (2017), no. 3, 1226–1252.
DOI: https://doi.org/10.2478/tmmp-2024-0005 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 25 - 44
Submitted on: Jan 21, 2022
Accepted on: Dec 3, 2023
Published on: Apr 13, 2024
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 El-Hacène Chalabi, Salim Mesbahi, Amar Ouaoua, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.