Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 582645, 17 pages
http://dx.doi.org/10.1155/2012/582645
Research Article

Stochastic PDEs and Infinite Horizon Backward Doubly Stochastic Differential Equations

1School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
2Shandong University of Art and Design, Jinan 250014, China

Received 12 May 2012; Accepted 26 November 2012

Academic Editor: Shiping Lu

Copyright © 2012 Bo Zhu and Baoyan Han. 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. E. Pardoux and S. Peng, “Backward doubly stochastic differential equations and systems of quasilinear SPDEs,” Probability Theory and Related Fields, vol. 98, no. 2, pp. 209–227, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. V. Bally and A. Matoussi, “Weak solutions for SPDEs and backward doubly stochastic differential equations,” Journal of Theoretical Probability, vol. 14, no. 1, pp. 125–164, 2001. View at Publisher · View at Google Scholar
  3. R. Buckdahn and J. Ma, “Stochastic viscosity solutions for nonlinear stochastic partial differential equations. I,” Stochastic Processes and their Applications, vol. 93, no. 2, pp. 181–204, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. R. Buckdahn and J. Ma, “Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II,” Stochastic Processes and their Applications, vol. 93, no. 2, pp. 205–228, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. E. Pardoux, Stochastic Partial Differential Equations, Fudan lecture notes, 2007.
  6. S. Peng and Y. Shi, “A type of time-symmetric forward-backward stochastic differential equations,” Comptes Rendus de l'Académie des Sciences—Series I, vol. 336, no. 9, pp. 773–778, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. Kunita, Stochastic Flows and Stochastic Differential Equations, vol. 24 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990.
  8. Y. Ren, A. Lin, and L. Hu, “Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 901–907, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. Q. Zhu, Y. Shi, and X. Gong, “Solutions to general forward-backward doubly stochastic differential equations,” Applied Mathematics and Mechanics, vol. 30, no. 4, pp. 517–526, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. Zhu and B. Y. Han, “Backward doubly stochastic differential equations with non-Lipschitz coefficients,” Acta Mathematica Scientia Series A, vol. 28, no. 5, pp. 977–984, 2008. View at Google Scholar · View at Zentralblatt MATH
  11. B. Zhu and B. Han, “Comparison theorems for the multidimensional BDSDEs and applications,” Journal of Applied Mathematics, vol. 2012, Article ID 304781, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. B. Boufoussi, J. van Casteren, and N. Mrhardy, “Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions,” Bernoulli, vol. 13, no. 2, pp. 423–446, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. L. Hu and Y. Ren, “Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes,” Journal of Computational and Applied Mathematics, vol. 229, no. 1, pp. 230–239, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Q. Zhang and H. Zhao, “Stationary solutions of SPDEs and infinite horizon BDSDEs,” Journal of Functional Analysis, vol. 252, no. 1, pp. 171–219, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. Zhu and B. Han, “Backward doubly stochastic differential equations with infinite time horizon,” Applications of Mathematics, vol. 57, no. 6, pp. 641–653, 2012. View at Google Scholar