- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 469390, 9 pages
Necessary Conditions for Optimality for Stochastic Evolution Equations
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Received 2 May 2013; Accepted 14 August 2013
Academic Editor: Fuding Xie
Copyright © 2013 AbdulRahman Al-Hussein. 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.
- A. Al-Hussein, “Sufficient conditions of optimality for backward stochastic evolution equations,” Communications on Stochastic Analysis, vol. 4, no. 3, pp. 433–442, 2010.
- A. Al-Hussein, “Suffcient conditions for optimality for stochastic evolution equations,” Statistics & Probability Letters, vol. 839, pp. 2103–2107, 2013.
- Y. Hu and S. Peng, “Maximum principle for optimal control of stochastic system of functional type,” Stochastic Analysis and Applications, vol. 14, no. 3, pp. 283–301, 1996.
- B. Øksendal, “Optimal control of stochastic partial differential equations,” Stochastic Analysis and Applications, vol. 23, no. 1, pp. 165–179, 2005.
- B. Øksendal, F. Proske, and T. Zhang, “Backward stochastic partial differential equations with jumps and application to optimal control of random jump fields,” Stochastics, vol. 77, no. 5, pp. 381–399, 2005.
- S. Peng, “Backward stochastic differential equations and applications to optimal control,” Applied Mathematics and Optimization, vol. 27, no. 2, pp. 125–144, 1993.
- J. Yong and X. Y. Zhou, Stochastic Controls. Hamiltonian Systems and HJB Equations, vol. 43 of Applications of Mathematics, Springer, New York, NY, USA, 1999.
- A. Al-Hussein, “Necessary conditions for optimal control of stochastic evolution equations in Hilbert spaces,” Applied Mathematics and Optimization, vol. 63, no. 3, pp. 385–400, 2011.
- A. Al-Hussein, “Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications,” Stochastics, vol. 81, no. 6, pp. 601–626, 2009.
- A. Debussche, Y. Hu, and G. Tessitore, “Ergodic BSDEs under weak dissipative assumptions,” Stochastic Processes and their Applications, vol. 121, no. 3, pp. 407–426, 2011.
- S. Cerrai, Second Order PDE's in Finite and Infinite Dimension. A Probabilistic Approach, vol. 1762 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2001.
- M. Fuhrman, Y. Hu, and G. Tessitore, “Stochastic maximum principle for optimal control of SPDEs,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 350, no. 13-14, pp. 683–688, 2012.
- A. Al-Hussein, “Martingale representation theorem in infinite dimensions,” Arab Journal of Mathematical Sciences, vol. 10, no. 1, pp. 1–18, 2004.
- G. Da Prato and J. Zabczyk, Second Order Partial Differential Equations in Hilbert Spaces, vol. 293 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 2002.
- A. Ichikawa, “Stability of semilinear stochastic evolution equations,” Journal of Mathematical Analysis and Applications, vol. 90, no. 1, pp. 12–44, 1982.
- A. Al-Hussein, “Time-dependent backward stochastic evolution equations,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 30, no. 2, pp. 159–183, 2007.
- Y. Hu and S. G. Peng, “Adapted solution of a backward semilinear stochastic evolution equation,” Stochastic Analysis and Applications, vol. 9, no. 4, pp. 445–459, 1991.
- G. Tessitore, “Existence, uniqueness and space regularity of the adapted solutions of a backward SPDE,” Stochastic Analysis and Applications, vol. 14, no. 4, pp. 461–486, 1996.
- A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, UK, 1992.