Table of Contents
Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 98764, 16 pages
http://dx.doi.org/10.1155/JAMSA/2006/98764

Classical solutions of linear regulator for degenerate diffusions

Department of Statistics, Shah Jalal University of Science and Technology, Sylhet 3114, Bangladesh

Received 26 November 2005; Revised 19 April 2006; Accepted 25 April 2006

Copyright © 2006 Md. Azizul Baten. 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. T. M. Apostol, Mathematical Analysis, Addison-Wesley, Massachusetts, 1974. View at Zentralblatt MATH · View at MathSciNet
  2. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems & Control: Foundations & Applications, Birkhäuser Boston, Massachusetts, 1997. View at Zentralblatt MATH · View at MathSciNet
  3. R. Bellman, Dynamic Programming, Princeton Univeristy Press, New Jersey, 1957. View at MathSciNet
  4. A. Bensoussan, Stochastic Control by Functional Analysis Methods, vol. 11 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, 1982. View at Zentralblatt MATH · View at MathSciNet
  5. F. H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, New York, 1983. View at Zentralblatt MATH · View at MathSciNet
  6. M. G. Crandall, H. Ishii, and P.-L. Lions, “User's guide to viscosity solutions of second order partial differential equations,” American Mathematical Society. Bulletin. New Series, vol. 27, no. 1, pp. 1–67, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. G. Crandall and P.-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations,” Transactions of the American Mathematical Society, vol. 277, no. 1, pp. 1–42, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. Da Prato, “Direct solution of a Riccati equation arising in stochastic control theory,” Applied Mathematics and Optimization, vol. 11, no. 3, pp. 191–208, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, vol. 25 of Applications of Mathematics (New York), Springer, New York, 1993. View at Zentralblatt MATH · View at MathSciNet
  10. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, vol. 24 of North-Holland Mathematical Library, North-Holland, Amsterdam, 1981. View at Zentralblatt MATH · View at MathSciNet
  11. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, vol. 113 of Graduate Texts in Mathematics, Springer, New York, 1988. View at Zentralblatt MATH · View at MathSciNet
  12. S. Koike and H. Morimoto, “Variational inequalities for leavable bounded-velocity control,” Applied Mathematics and Optimization, vol. 48, no. 1, pp. 1–20, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. P.-L. Lions, “Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. II. Viscosity solutions and uniqueness,” Communications in Partial Differential Equations, vol. 8, no. 11, pp. 1229–1276, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J.-L. Menaldi and M. Robin, “On some cheap control problems for diffusion processes,” Transactions of the American Mathematical Society, vol. 278, no. 2, pp. 771–802, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Nisio, Lectures on Stochastic Control Theory, vol. 9 of ISI Lecture Notes, MacMillan, New Delhi, 1981. View at Zentralblatt MATH · View at MathSciNet