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Original Articles

Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

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Pages 2371-2384 | Received 10 Aug 2013, Accepted 29 Oct 2013, Published online: 22 Jun 2015

References

  • Amerio, L., Prouse, G. (1971). Almost-Periodic Functions and Functional Equations. New York: Van Nostrand Reinhold.
  • Arnold, L., Tudor, C. (1998). Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Stochastics: Int. J. Prob. Stochastic Processes. 64(3–4): 177–193.
  • Bezandry, P.H., Diagana, T. (2011). Almost Periodic Stochastic Processes. New York: Springer.
  • Bochner, S. (1964). Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. Sci. U.S.A. 52(4): 907.
  • Chen, Z., Wu, P., Li, B. (2013). A strong law of large numbers for non-additive probabilities. Int. J. Approximate Reasoning
  • Corduneanu, C. (1989). Almost Periodic Functions. New York: Chelsea.
  • Cui, J., Yan, L. (2012). On almost automorphic mild solutions for nonautonomous stochastic evolution equations. : T. Diagana, ed. Abstract and Applied Analysis (Vol. 2012). Hindawi Publishing Corporation.
  • Da Prato, G., Tudor, C. (1995). Periodic and almost periodic solutions for semilinear stochastic equations. Stochastic Anal. Appl. 13(1): 13–33.
  • Denis, L., Hu, M., Peng, S. (2011). Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal. 34(2): 139–161.
  • Fink, A. (1974). Almost Periodic Differential Equations, Vol. 37, Lecture Notes in Math. Berlin: Springer-Verlag.
  • Gao, F. (2009). Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion. Stochastic Processes Appl. 119(10): 3356–3382.
  • Goldstein, J.A. (1979). Convexity, boundedness, and almost periodicity for differential equations in Hillbert space. Int. J. Math. Math. Sci. 2(1): 1–13.
  • Hu, F., Zhang, D. (2010). Central limit theorem for capacities. Comptes Rendus Mathematique. 348(19): 1111–1114.
  • Hu, M., Ji, S., Peng, S., Song, Y. (2012). Backward stochastic differential equations driven by G-Brownian Motion. arXiv preprint arXiv:1206.5889.
  • Hu, M., Peng, S. (2009). On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math. Appl. Sin., Eng. Ser. 25(3): 539–546.
  • Li, X., Peng, S. (2011). Stopping times and related Itô’s calculus with G-Brownian motion. Stochastic Processes Appl. 121(7): 1492–1508.
  • Lin, Q. (2013). Local time and Tanaka formula for the G-Brownian motion. J. Math. Anal. Appl.
  • Lin, Y., Bai, X. (2010). On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients. Acta Math. Appl. Sin. Eng. Ser. appear. arXiv, 1002.
  • Peng, S. (2006). G-Expectation, G-Brownian motion and related stochastic calculus of Itô’s type. In: Benth et al., eds. Proceedings of the 2005 Abel Symposium. Berlin: Springer-Verlag. pp. 541–567.
  • Peng, S. (2010). Nonlinear expectations and stochastic calculus under uncertainty. arXiv preprint arXiv:1002.4546.
  • Ren, Y., Bi, Q., Sakthivel, R. (2013). Stochastic functional differential equations with infinite delay driven by G-Brownian motion. Math. Methods Appl. Sci. 36(13):1746–1759.
  • Song, Y. (2012). Uniqueness of the representation for G-martingales with finite variation. Electron. J. Prob. 17(24): 1–15.
  • Tudor, C. (1992). Almost periodic solutions of affine stochastic evolution equations. Stochastics: Int. J. Prob. Stochastic Processes. 38(4): 251–266.
  • Wang, Y., Liu, Z. (2012). Almost periodic solutions for stochastic differential equations with Levy noise. Nonlinearity. 25(10): 2803.
  • Xu, J., Zhang, B. (2009). Martingale characterization of G-Brownian motion. Stochastic Processes Appl. 119(1): 232–248.
  • Zaidman, S. (1985). Almost-periodic Functions in Abstract Spaces. (Vol. 126). Marshfield, MA: Pitman Advanced Pub. Program.
  • Zhang, B., Xu, J., Kannan, D. (2010). Extension and application of Itô’s formula under G-framework. Stochastic Anal. Appl. 28(2): 322–349.
  • Zhang, D., Chen, Z. (2012). Exponential stability for stochastic differential equation driven by G-Brownian motion. Appl. Math. Lett. 25(11): 1906–1910.

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