Stability of square-mean almost automorphic mild solutions to impulsive stochastic differential equations driven by G-Brownian motion

References

• Bezandry, P., & Diagana, T. (2007). Existence of almost periodic solutions to some stochastic differential equations. Applicable Analysis, 86(7), 819–827. doi: 10.1080/00036810701397788
   Web of Science ®Google Scholar
• Chang, Y., Zhao, Z., & N'Guérékata, G. (2011). Square-mean almost automorphic mild solutions to non-autonomous stochastic differential equations in Hilbert spaces. Computers and Mathematics with Applications, 61(12), 384–391. doi: 10.1016/j.camwa.2010.11.014
   Google Scholar
• Denis, L., Hu, M., & Peng, S. (2011). Function spaces and capacity related to a sublinear expectation: Application to G-Brownian motion pathes. Potential Analysis, 34(2), 139–161. doi: 10.1007/s11118-010-9185-x
   Web of Science ®Google Scholar
• Fei, W., & Fei, C. (2013). Exponential stability for stochastic differential equations disturbed by G-Brownian motion. arXiv:1311.7311.
   Google Scholar
• Fu, M., & Liu, Z. (2010). Square-mean almost automorphic solutions of some stochastic differential equations. Proceedings of the American Mathematical Society, 138(10), 3689–3701. doi: 10.1090/S0002-9939-10-10377-3
   Web of Science ®Google Scholar
• Gao, F. (2009). Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion. Stochastic Processes and their Applications, 119(10), 3356–3382. doi: 10.1016/j.spa.2009.05.010
   Web of Science ®Google Scholar
• Gu, Y., Ren, Y., & Sakthivel, R. (2016). Square-mean pseudo almost automorphic mild solutions for stochastic evolution equations driven by G-Brownian motion. Stochastic Analysis and Applications, 34(3), 528–545. doi: 10.1080/07362994.2016.1155159
   Web of Science ®Google Scholar
• Hu, F. (2017). The modulus of continuity theorem for G -Brownian motion. Communications in Statistics - Theory and Methods, 46(7), 3586–3598. doi: 10.1080/03610926.2015.1066816
   Web of Science ®Google Scholar
• Hu, F., & Chen, Z (2016). General laws of large numbers under sublinear expectations. Communications in Statistics - Theory and Methods, 45(14), 4215–4229. doi: 10.1080/03610926.2014.917677
   Web of Science ®Google Scholar
• Hu, F., Chen, Z., & Wu, P (2016). A general strong law of large numbers for non-additive probabilities and its applications. Statisticss, 50(4), 733–749.
   Google Scholar
• Hu, F., Chen, Z., & Zhang, D (2014). How big are the increments of G-Brownian motion?. Science China Mathematics, 57(8), 1687–1700. doi: 10.1007/s11425-014-4816-0
   Web of Science ®Google Scholar
• Hu, M., & Peng, S. (2009). On the representation theorem of G-expectations and paths of G-Brownian motion. Acta Mathematicae Applicatae Sinica, English Series, 25(3), 539–546. doi: 10.1007/s10255-008-8831-1
   Web of Science ®Google Scholar
• Hu, L., Ren, Y., & Xu, T. (2014). p-moment stability of solutions to stochastic differential equations driven by G-Brownian motion. Applied Mathematics and Computation, 230, 231–237. doi: 10.1016/j.amc.2013.12.111
   Web of Science ®Google Scholar
• Lakshmikantham, V., Bainov, D., & Simeonov, P. (1989). Theory of impulsive differential equations. World Scientific: Singapore.
   Google Scholar
• Li, X., Lin, X., & Lin, Y. (2016). Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. Journal of Mathematical Analysis and Applications, 439(1), 235–255. doi: 10.1016/j.jmaa.2016.02.042
   Web of Science ®Google Scholar
• Lin, Y. (2013). Stochastic differential equations driven by G-Brownian motion with reflecting boundary conditions. Electronic Journal of Probability, 18(9), 1–23.
   Google Scholar
• Liu, B. (2008). Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Transactions on Automatic Control, 53(9), 2128–2133. doi: 10.1109/TAC.2008.930185
   Web of Science ®Google Scholar
• Liu, X. (1993). Impulsive stabilization of nonlinear systems. IMA Journal of Mathematical Control and Information, 10(1), 11–19. doi: 10.1093/imamci/10.1.11
   Web of Science ®Google Scholar
• Peng, P. (2007a). G-expectation, G-Brownian motion and related stochastic calculus of Itô type. Stochastic Analysis and Applications, 2, 541–567. doi: 10.1007/978-3-540-70847-6_25
   Google Scholar
• Peng, S. (2007b). G-Brownian motion and dynamic risk measures under volatility uncertainty. arXiv preprint arXiv:0711.2834.
   Google Scholar
• Peng, S. (2008). Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Processes and their Applications, 118(12), 2223–2253. doi: 10.1016/j.spa.2007.10.015
   Web of Science ®Google Scholar
• Peng, S., & Jia, B. (2010). Some criteria on p-th moment stability of impulsive stochastic functional differential equations. Statistics and Probability Letters, 80(13–14), 1085–1092. doi: 10.1016/j.spl.2010.03.002
   Web of Science ®Google Scholar
• Ren, Y., Bi, Q., & Sakthivel, R. (2013). Stochastic functional differential equations with infinite delay driven by G-Brownian motion. Mathematical Methods in the Applied Sciences, 36(13), 1746–1759. doi: 10.1002/mma.2720
   Web of Science ®Google Scholar
• Ren, Y., Jia, X., & Hu, L. (2015). Exponential stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion. Discrete and Continuous Dynamical Systems-Series B, 20(7), 2157–2169. doi: 10.3934/dcdsb.2015.20.2157
   Web of Science ®Google Scholar
• Ren, Y., Jia, X., & Sakthivel, R. (2017). The pth moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion. Applicable Analysis, 96(6), 988–1003. doi: 10.1080/00036811.2016.1169529
   Web of Science ®Google Scholar
• Ren, Y., Yin, W., & Zhu, D. (2018). Exponential stability of SDEs driven by G-Brownian motion with delayed impulsive effects: Average impulsive interval approach. Discrete and Continuous Dynamical Systems-Series B, 23(8), 3347–3360. doi: 10.3934/dcdsb.2018248
   Web of Science ®Google Scholar
• Shen, L., & Sun, J. (2011). p-th moment exponential stability of stochastic differential equations with impulsive effect. Information Sciences, 54, 1702–1711.
   Web of Science ®Google Scholar
• Wu, S., Han, D., & Meng, X. (2004). p-moment stability of stochastic differential equations with jumps. Applied mathematics and computation, 152(2), 505–519. doi: 10.1016/S0096-3003(03)00573-3
   Web of Science ®Google Scholar
• Wu, H., & Sun, J. (2006). p-moment stability of stochastic differential equations with impulsive jump and Markovian switching. Automatica, 42(10), 1753–1759. doi: 10.1016/j.automatica.2006.05.009
   Web of Science ®Google Scholar
• Wu, X., Yan, L., Zhang, W., & Chen, L. (2012). Exponential stability of impulsive stochastic delay differential systems. Discrete Dynamics in Nature and society, 2015, 1–15.
   Google Scholar
• Xu, L., & Ge, S. (2015). The p-moment exponential ultimate boundedness of implusive stochastic differential systems. Applied Mathematics Letters, 42, 22–29. doi: 10.1016/j.aml.2014.10.018
   Web of Science ®Google Scholar
• Xu, J., & Zhang, B. (2009). Martingale characterization of G-Brownian motion. Stochastic Processes and their Applications, 119(1), 232–248. doi: 10.1016/j.spa.2008.02.001
   Web of Science ®Google Scholar
• Zhang, D., & Chen, Z. (2012). Exponential stability for stochastic differential equations driven by G-Brownian motion. Applied Mathematics Letters, 25(11), 1906–1910. doi: 10.1016/j.aml.2012.02.063
   Web of Science ®Google Scholar
• Zhang, B., Xu, J., & Kannan, D. (2010). Extension and application of Itô's formula under G-Framework. Stochastic Analysis and Applications, 28(2), 322–349. doi: 10.1080/07362990903546595
   Web of Science ®Google Scholar