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Practical Stability with Respect to a Part of the Variables of Stochastic Differential Equations Driven by G-Brownian Motion

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Abstract

In this paper, practical stability with respect to a part of the variables of stochastic differential equations driven by G-Brownian motion (G-SDEs) is studied. The analysis of the global practical uniform p th moment exponential stability, as well as the global practical uniform exponential stability with respect to a part of the variables of G-SDEs, is investigated by means of the G-Lyapunov functions. An illustrative example to show the usefulness of the practical stability with respect to a part of the variables notion is also provided.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewer for valuable comments and suggestions, which allowed us to improve the paper.

Funding

The research of Tomás Caraballo has been partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) under the project PGC2018-096540-B-I00, and by Junta de Andalucía (Consejería de Economía y Conocimiento) and FEDER under projects US-1254251 and P18-FR-4509.

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Authors and Affiliations

  1. Departamento Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41008, Sevilla, Spain

    Tomás Caraballo

  2. Faculty of Sciences of Sfax, Department of Mathematics, University of Sfax, Sfax, Tunisia

    Faten Ezzine & Mohamed Ali Hammami

Authors
  1. Tomás Caraballo
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  2. Faten Ezzine
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  3. Mohamed Ali Hammami
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Correspondence to Mohamed Ali Hammami.

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Caraballo, T., Ezzine, F. & Hammami, M.A. Practical Stability with Respect to a Part of the Variables of Stochastic Differential Equations Driven by G-Brownian Motion. J Dyn Control Syst 29, 1–19 (2023). https://doi.org/10.1007/s10883-022-09593-2

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