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Partial Practical Exponential Stability of Neutral Stochastic Functional Differential Equations with Markovian Switching

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Abstract

In this paper, we investigate the partial practical exponential stability of neutral stochastic functional differential equations with Markovian switching. The main tool used to prove the results is the Lyapunov method. We analyze an illustrative example to show the applicability and interest of the main results.

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References

  1. Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley, New York (1974)

    MATH  Google Scholar 

  2. Caraballo, T., Hammami, M.A., Mchiri, L.: On the practical global uniform asymptotic stability of stochastic differential equations. Stochastics 88(1), 45–56 (2016)

    Article  MathSciNet  Google Scholar 

  3. Caraballo, T., Hammami, M.A., Mchiri, L.: Practical asymptotic stability of nonlinear stochastic evolution equations. Stoch. Anal. Appl. 32, 77–87 (2014)

    Article  MathSciNet  Google Scholar 

  4. Has’minskii, R. Z.: Stochastic Stability of Differential Equations. Sijthoff Noordhoff (1980)

  5. Ignatyev, O.A.: Partial asymptotic stability in probability of stochastic differential equations. Stat. Probab. Lett. 79, 597–601 (2009)

    Article  MathSciNet  Google Scholar 

  6. Liu, D., Wang, W., Ignatyev, O., Zhang, W.: Partial stochastic asymptotic stability of neutral stochastic functional differential equations with Markovian switching by boundary condition. Adv. Differ. Equ. 220, 1–8 (2012). https://doi.org/10.1186/1687-1847-2012-220

    Article  MathSciNet  MATH  Google Scholar 

  7. Mao, X., Yuan, C.: Stochastic Differential Equations with Markovian Switching. Imperial College Press, London (2006)

    Book  Google Scholar 

  8. Mao, X.: Exponential Stability of Stochastic Differential Equations. Marcel Dekker Inc, New York (1994)

    MATH  Google Scholar 

  9. Mao, X.: Stochastic Differential Equations and Applications. Ellis Horwood, Chichester (1997)

    MATH  Google Scholar 

  10. Obradović, M., Milošević, M.: Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler–Maruyama method. J. Comput. Appl. Math. 309, 244–266 (2017)

    Article  MathSciNet  Google Scholar 

  11. Song, R., Lu, B., Zhu, Q.: Stability of a class of neutral stochastic functional differential equations with Markovian switching. IET Control Theory Appl. 12(15), 2043–2054 (2018)

    Article  MathSciNet  Google Scholar 

  12. Sharov, V.F.: Partial stability and stabilization of stochastic systems. Avtom. Telemekh. 11, 63–71 (1978)

    MathSciNet  Google Scholar 

  13. Vorotnikov, V.I.: Partial Stability and Control. Birkhauser, Boston (1998)

    MATH  Google Scholar 

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Acknowledgements

The research of T. C. has been partially supported by Ministerio de Ciencia, Innovación y Universidades (Spain), FEDER (European Community) under grant PGC2018-096540-B-I00, and Junta de Andalucía (Spain) under grant US-1254251. Lassad Mchiri and Mohamed Rhaima extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research gourp No. RG-1441-328.

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012, Sevilla, Spain

    Tomás Caraballo

  2. Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh, Saudi Arabia

    Lassaad Mchiri & Mohamed Rhaima

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

    Lassaad Mchiri

  4. Faculty of Sciences of Tunis, Department of Mathematics, University of Tunis Manar, Tunis, Tunisia

    Mohamed Rhaima

Authors
  1. Tomás Caraballo
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  2. Lassaad Mchiri
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  3. Mohamed Rhaima
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Correspondence to Tomás Caraballo.

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Caraballo, T., Mchiri, L. & Rhaima, M. Partial Practical Exponential Stability of Neutral Stochastic Functional Differential Equations with Markovian Switching. Mediterr. J. Math. 18, 142 (2021). https://doi.org/10.1007/s00009-021-01786-6

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  • DOI: https://doi.org/10.1007/s00009-021-01786-6

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