Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2010 (2010), Article ID 425762, 26 pages
http://dx.doi.org/10.1155/2010/425762
Research Article

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

1School of Management, Huazhong University of Science and Technology, Wuhan 430074, China
2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 17 June 2010; Revised 14 September 2010; Accepted 18 September 2010

Academic Editor: Neville Ford

Copyright © 2010 Minggao Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. X. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, Chichester, UK, 1997.
  2. X. Mao, “Razumikhin-type theorems on exponential stability of stochastic functional-differential equations,” Stochastic Processes and Their Applications, vol. 65, no. 2, pp. 233–250, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. X. Mao, “A note on the LaSalle-type theorems for stochastic differential delay equations,” Journal of Mathematical Analysis and Applications, vol. 268, no. 1, pp. 125–142, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. X. Mao, “The LaSalle-type theorems for stochastic functional differential equations,” Nonlinear Studies, vol. 7, no. 2, pp. 307–328, 2000. View at Google Scholar · View at Zentralblatt MATH
  5. X. Mao, “Razumikhin-type theorems on exponential stability of neutral stochastic functional-differential equations,” SIAM Journal on Mathematical Analysis, vol. 28, no. 2, pp. 389–401, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. Zhou, Z. Wang, and D. Feng, “Stochastic functional differential equations with infinite delay,” Journal of Mathematical Analysis and Applications, vol. 357, no. 2, pp. 416–426, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. Zhou and S. Hu, “Razumikhin-type theorems of neutral stochastic functional differential equations,” Acta Mathematica Scientia. Series B, vol. 29, no. 1, pp. 181–190, 2009. View at Publisher · View at Google Scholar
  8. L. Yue, X. Meng, and F. Wu, “General decay stability for stochastic functional differential equations with infinite delay,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2010, Article ID 875908, 17 pages, 2010. View at Publisher · View at Google Scholar
  9. Y. Shen, Q. Luo, and X. Mao, “The improved LaSalle-type theorems for stochastic functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 134–154, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. Z. Khasminskii, Stochastic Stability of Differential Equations, vol. 7 of Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
  11. X. Mao and M. J. Rassias, “Khasminskii-type theorems for stochastic differential delay equations,” Stochastic Analysis and Applications, vol. 23, no. 5, pp. 1045–1069, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. X. Mao, Exponential Stability of Stochastic Differential Equations, vol. 182 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1994.
  13. X. Mao, Stochastic Differential Equations with Markovian Switching, 2005.
  14. F. Wu, S. Hu, and C. Huang, “Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay,” System and Control Letter, vol. 59, no. 3-4, pp. 195–202, 2010. View at Publisher · View at Google Scholar
  15. S. Hu, C. Huang, and F. Wu, Sochastic Differential Equations, The Science Publishing, Beijing, China, 2008.