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

El-Hacène Chalabi; Salim Mesbahi; Amar Ouaoua

doi:10.2478/tmmp-2024-0005

.blurhash-client-img { display: none !important; }

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

Tatra Mountains Mathematical Publications

Volume 88 (2024): Issue 3 (December 2024)

By: El-Hacène Chalabi, Salim Mesbahi and Amar Ouaoua

Open Access

|Apr 2024

Abstract

In this article, we are interested in the study of a class of stochastic functional differential systems driven by G-Brownian motion with infinite delay. We prove the existence and uniqueness of the solutions when two basic conditions are met: the linear growth condition and the Lipschitz condition.

References

BAO, H.—JIANG, D.: Existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in L^p(Ω,C_h), Stoch. Dyn. 9 (2009), no. 4, 597–612. DOI:10.1142/s0219493709002786.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
KOLÁŘOVÁ, E.: Applications of second order stochastic integral equations to electrical networks, Tatra Mt. Math. Publ. 63 (2015), 163–173.
Search in Google Scholar Back to article
KOLÁŘOVÁ, E.—BRANĆIK, L.: Stochastic Differential Equations Describing Systems with Coloured Noise, Tatra Mt. Math. Publ. 71 (2018), 107–99.
Search in Google Scholar Back to article
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
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
PENG, S.: Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stochastic Process. Appl. 118 (2008), no. 12, 2223–2253.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
WU, F.—YIN, G.—MEI, H.: Stochastic functional differential equations with infinite delay, J. Differential Equations 262 (2017), no. 3, 1226–1252.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2024-0005 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

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: 1 issue per year

Keywords:

G-expectation,

G-Brownian motion,

G-stochastic differential equations,

infinite delay

Related subjects:

Mathematics,

General mathematics

© 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.

Volume 88 (2024): Issue 3 (December 2024)