Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 22, 1991 - Issue 4
20
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

ε-optimal control of random parabolic differential equations by an elliptic approximation

Pages 621-634 | Received 01 Mar 1990, Published online: 27 Jun 2007

References

  • Ahmed , N.U. 1983 . Stochastic control on HILBERT space for linear evolution equations with random operator-valued coefficients . SIAM J. Contr. Opt , 19 ( 3 ) : 401 – 430 .
  • Bensoussan , A. 1983 . Stochastic maximum principle for distributed parameter systems . J. Franklin Inst , 315 ( 5-6 ) : 387 – 406 .
  • Curtain , R.F. and Pritchard , A.J. 1978 . Infinite dimensional linear systems theory . Lect. Notes Contr. Inf. ScL , 8 ( 5-6 )
  • Da Prato , G. and Ichikawa , A. 1985 . Stability and quadratic control for linear stochastic equations with unbounded coefficients . Bolletino U.M., I , 4-B ( 6 ) : 987 – 1001 .
  • Grecksch , W. 1987 . Finite dimensional approximation of an optimal control problem for random partial differential equations . Lect. Notes Contr. Inf. ScL , 96 ( 6 ) : 294 – 300 .
  • Grecksch , W. 1987 . “ Stochastische Evolutionsgleichungen und deren Steuerung ” . In Teubner-Texte zur Mathematik , Vol. 98 , Leipzig : BSB B.G. Teubner Verlagsgesellschaft .
  • Grecksch , W. 1987 . ε-optimale Steuerung einer linearen parabolischen Itogleichung . Math. Nach-richten , 134 : 7 – 20 .
  • Grecksch , W. 1989 . A prediction problem for a time discrete parabolic ITO equation . Mathematical Research , 54 : 65 – 76 .
  • Grecksch , W. 1989 . An elliptical approximation of a parabolic ITO equation . Probability Theory and Related Fields , 54
  • Karabaš , M.A. 1987 . O nepreryvnoj zavisimosti reśenij stochastičeskich uravnenij s monotonnymi koefficentami ot upravlenija . Teorija slucajnych processov , 15 : 37 – 40 .
  • Krylov , N.V. and Rozovsku , B.L. 1979 . Ob evoljucionnych stochasticeskich uravnenijach . Itog i nauki i techniki , 14 : 71 – 146 .
  • Tudor , D. 1988 . Quadratic control for linear stochastic evolution equations . Studii si cercetari matematice (extras) , 40 ( 3 ) : 259 – 276 .
  • Tudor , C. 1989 . ε-OptimaI control for semilinear stochastic evolution equations . Appl. Math. Opt , 20 ( 3 ) : 319 – 331 .
  • Zeidler , E. 1977 . “ Vorlesungen über nichtlineare Funktionalanalysis II — Monotone Operatoren ” . In Teubner-Texte zur Mathematik , Leipzig : BSB B. G. Teubner Verlagsgesellschaft .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.