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Stability with respect to a part of the variables of stochastic dierential equations driven by G-Brownian motion
  • Tomas Caraballo,
  • Faten Ezzine,
  • Mohamed Ali Hammami
Tomas Caraballo
Universidad de Sevilla
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Faten Ezzine
University of Sfax Faculty of Sciences of Sfax
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Mohamed Ali Hammami
University of Sfax Faculty of Sciences of Sfax
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Abstract

In this paper, we investigate the pth moment exponential stability of stochastic differential equations driven by G-Brownian motion (G-SDEs) with respect to a part of the variables by means of the G-Lyapunov functions and Gronwall’s inequalities. We establish sufficient conditions to ensure the quasi sure exponential stability of stochastic differential equations perturbed by G-Brownian motion with respect to a part of the variables. Some illustrative examples to show the usefulness of the stability with respect to a part of variables notion are also provided.