Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 903912, 10 pages
http://dx.doi.org/10.1155/2014/903912
Research Article

On Optimal Control Problem for Backward Stochastic Doubly Systems

Laboratory of Applied Mathematics, University Mouhamed Khider, P.O. Box 145, 07000 Biskra, Algeria

Received 15 December 2013; Accepted 16 January 2014; Published 4 March 2014

Academic Editors: F. Jauberteau and F. Sartoretto

Copyright © 2014 Adel Chala. 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. G. 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 MathSciNet
  2. Y. Shi, Y. Gu, and K. Liu, “Comparison theorems of backward doubly stochastic differential equations and applications,” Stochastic Analysis and Applications, vol. 23, no. 1, pp. 97–110, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. N'zi and J. M. Owo, “Backward doubly stochastic differential equations with discontinuous coefficients,” Statistics & Probability Letters, vol. 79, no. 7, pp. 920–926, 2009. View at Google Scholar
  4. S. Peng and Y. A. Shi, “A type of time-symmetric forward-backward stochastic differential equations,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 336, no. 9, pp. 773–778, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. N'zi and J.-M. Owo, “Backward doubly stochastic differential equations with non-Lipschitz coefficients,” Random Operators and Stochastic Equations, vol. 16, no. 4, pp. 307–324, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. Bahlali, “Necessary and sufficient optimality conditions for relaxed and strict control problems,” SIAM Journal on Control and Optimization, vol. 47, no. 4, pp. 2078–2095, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Bahlali and A. Chala, “A general optimality conditions for stochastic control problems of jump diffusions,” Applied Mathematics and Optimization, vol. 65, no. 1, pp. 15–29, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. Chala, “The relaxed optimal control problem of forward-backward stochastic doubly systems with Poisson jumps and its application to LQ problem,” Random Operators and Stochastic Equations, vol. 20, no. 3, pp. 255–282, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Mezerdi and S. Bahlali, “Necessary conditions for optimality in relaxed stochastic control problems,” Stochastics and Stochastics Reports, vol. 73, no. 3-4, pp. 201–218, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Bahlali and B. Gherbal, “Optimality conditions of controlled backward doubly stochastic differential equations,” Random Operators and Stochastic Equations, vol. 18, no. 3, pp. 247–265, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  11. Y. Han, S. Peng, and Z. Wu, “Maximum principle for backward doubly stochastic control systems with applications,” SIAM Journal on Control and Optimization, vol. 48, no. 7, pp. 4224–4241, 2010. View at Publisher · View at Google Scholar · View at MathSciNet