Stepanov-like almost automorphic solutions for stochastic differential equations with Lévy noise

References

• Ahmad, S. 1988. On almost periodic solutions of the competing species problems. Proceedings of the American Mathematical Society 102 (4):855–61.
   Web of Science ®Google Scholar
• Arnold, L., and C. Tudor, 1998. Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Stochastics and Stochastics Reports 64:177–93.
   Google Scholar
• Bochner, S. 1962. Uniform convergence of monotone sequences of functions. Proceedings of the National Academy of Sciences 47:582–5.
   Web of Science ®Google Scholar
• Bochner, S. 1964. Continuous mappings of almost automorphic and almost periodic functions. Proceedings of the National Academy of Sciences 52:907–10.
   PubMed Web of Science ®Google Scholar
• Bezandry, P., and T. Diagana, 2008. Existence of S2 almost periodic solutions to a class of nonautonomous stochastic evolution equations. Electronic Journal of Qualitative Theory of Differential Equations 35:1–19.
   Google Scholar
• Corduneanu, C. 2009. Almost periodic oscillations and waves. New York: Springer.
   Google Scholar
• Cont, R., and P. Tankov, 2004. Financial modelling with jump processes. Financial Mathematics Series. Boca Raton: Chapman and Hall/CRC.
   Google Scholar
• Cao, J., Q. Yang, and Z. Huang. On almost periodic mild solutions for stochastic functional differential equations. Nonlinear Analysis 13:275–86.
   Google Scholar
• Chang, Y. K., Z. H. Zhao, G. M. N’Guérékata, and R. Ma, 2011. Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations. Nonlinear Analysis: Real World Applications 12:1130–9.
   Web of Science ®Google Scholar
• Doss, R. 1962. On generalized almost periodic functions-II. Journal of the London Mathematical Society 37:133–40.
   Google Scholar
• Diagana, T., and G. M. N’Guérékata, 2007. Stepanov-like almost automorphic functions and applications to some semilinear equations. Applied Analysis 86:723–33.
   Web of Science ®Google Scholar
• Da Prato, G., and C. Tudor, 1995. Periodic and almost periodic solutions for semilinear stochastic equations. Stochastic Analysis and Applications 13:13–33.
   Web of Science ®Google Scholar
• Da Prato, G., and J. Zabczyk, 1992. Stochastic equations in infinite dimensions. Vol. 44 of Encyclopedia of mathematics and its applications. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Fink, A. M. 1974. Almost periodic differential equations. Berlin: Springer.
   Google Scholar
• Fu, M., and Z. Liu, 2010. Square-mean almost automorphic solutions for some stochastic differential equations. Proceedings of the American Mathematical Society 138:3689–701.
   Web of Science ®Google Scholar
• Hewitt, E. 1953. Linear functionals on almost periodic functions. Transactions of the American Mathematical Society 74:303–22.
   Web of Science ®Google Scholar
• Halanay, A. 1987. Periodic and almost periodic solutions to affine stochastic systems. In Proceedings of the Eleventh International Conference on Nonlinear Oscillations, Budapest, János Bolyai Math. Soc., Budapest. 1987:94–101.
   Google Scholar
• Hernández, E., and H. R. Henríquez, 1998. Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. Journal of Mathematical Analysis and Applications 221:499–522.
   Web of Science ®Google Scholar
• Henríquez, H. R., and C. H. Vasquez, 1999. Almost periodic solutions of abstract retarded functional-differential equations with unbounded delay. Acta Applicandae Mathematicae 57:105–32.
   Web of Science ®Google Scholar
• Ichikawa, A. 1982. Stability of semilinear stochastic evolution equations. Journal of Mathematical Analysis and Applications 90:12–44.
   Web of Science ®Google Scholar
• Kundert, K. S., G. B. Sorkin, and A. Sangiovanni–Vincentelli, 1988. Applying harmonic balance to almost-periodic circuits. The IEEE Transactions on Microwave Theory 36 (2):366–78.
   Web of Science ®Google Scholar
• Lee, H., and H. Alkahby, 2008. Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay. Nonlinear Analysis 69:2158–66.
   Web of Science ®Google Scholar
• Li, Z., J. Luo, and K. Liu, 2014. On almost periodic mild solutions for neutral stochastic evolution equations with infinite delay. Nonlinear Analysis 10:182–90.
   Web of Science ®Google Scholar
• Liu, Z., and K. Sun, 2014. Almost automorphic solutions for stochastic differential equations driven by Lévy noise. Journal of Functional Analysis 266:1115–49.
   Web of Science ®Google Scholar
• Liu, D., W. Wang, and J. L. MenaIdi. 2015. Almost sure asymptotic stabilization of differential equations with time-varying delay by Lévy noise. Nonlinear Dynamics. 79 (1):163–172. DOI 10.1007/s11071-014-1653-1.
   Web of Science ®Google Scholar
• Mishra, I., and D. Bahuguna, 2013. Weighted pseudo almost automorphic solution of an integro-differential equation, with weighted Stepanov-like pseudo almost automorphic forcing term. Applied Mathematics and Computation 219:5345–55.
   Web of Science ®Google Scholar
• N’Guérékata, G. M. 2001. Almost automorphic and almost periodic functions in abstract space. New York, London, Moscow: Kluwer Academic Plenum Publishers.
   Google Scholar
• N’Guérékata, G. M. 2005. Topics in almost automorphy. New York, Boston, Dordrecht, London, Moscow: Springer.
   Google Scholar
• N’Guérékata, G. M., and A. Pankov, 2008. Stepanov-like almost automorphic functions and monotone evolution equations. Nonlinear Analysis 68:2658–67.
   Web of Science ®Google Scholar
• Peszat, S., and J. Zabczyk. Stochastic partial differential equations with Lévy noise. Cambridge: Cambridge University Press.
   Google Scholar
• Revathi, P., R. Stakthivel, Y. Ren, and S. M. Anthoni, 2014. Existence of almost automorphic mild solutions to non-autonomous neutral stochastic differential equations. Applied Mathematics and Computation 230:639–49.
   Web of Science ®Google Scholar
• Ren, Y., Q. Zhou, and L. Chen, 2011. Existence, uniqueness and stability of mild solutions for time-dependent stochastic evolution equations with poisson jumps and infinite delay. The Journal of Optimization Theory and Applications 149:315–31.
   Web of Science ®Google Scholar
• Tudor, C. 1992. Almost periodic solutions of affine stochastic evolution equations. Stochastics and Stochastics Reports 38:251–66.
   Google Scholar
• Taniguchi, T., and J. Luo, 2009. The existence and asymptotic behavior of mild solutions for stochastic evolution equations with infinite delays driven by Poisson jumps. Stochastics and Dynamics 9:217–29.
   Web of Science ®Google Scholar
• Wang, Y., and Z. Liu, 2012. Almost periodic solutions for stochastic differential equations with Lévy noise. Nonlinearity 25:2803–21.
   Web of Science ®Google Scholar
• Yang, F. L., and C. Y. Zhang, 2011. Remotely almost periodic solutions to parabolic boundary value inverse problems. Taiwanese Journal of Mathematics 15:43–57.
   Web of Science ®Google Scholar
• Zhao, Z. H., Y. K. Chang, and J. J. Nieto, 2010. Almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equation in Banach spaces. Nonlinear Analysis TMA 72:1886–94.
   Web of Science ®Google Scholar