On ergodic control of stochastic evolution equations

References

• Bielecki , T. and Stettner , L. 1989 . On ergodic control problems for singularly perturbed Markov processes . JAMO , 20 : 131 – 161 .
   Google Scholar
• Bismut , M. 1976 . Theorie probabiliste du controle des diffusions . Mem. Amer. Math. Soc , 4 ( 167 )
   Google Scholar
• Borkar , V.S. and Govindan , T.E. 1994 . Optimal control of semilinear stochastic evolution equations . Nonlinear Analysis, Theory, Methods & Appl , 23 ( 167 ) : 15 – 35 .
   Google Scholar
• Cannarsa , P. and Da Prato , G. 1989 . Second order Hamilton Jacobi Bellman equations and nonlinear stochastic control in infinite dimensions . Preprints di Matematica , 54 ( 167 )
   Google Scholar
• Da Prato , G. , Gatarek , D. and Zabczyk , J. 1992 . Invariant measures for semilinear stochastic equations . Stoch. Anal. Appl , 10 ( 167 ) : 387 – 408 .
   Google Scholar
• Da Prato , G. and Zabczyk , J. 1992 . Stochastic equations in infinite dimensions , Cambridge University Press .
   Google Scholar
• Edwards , R.E. 1965 . Functional Analysis, Theory and Applications , New York : Holt, Rinehart and Winston .
   Google Scholar
• Gatarek D. Goldys B. Optimal control in the Mayer problem for stochastic reaction - diffusion equations TReport No. S92-2 School of Mathematics The University of New South Wales 1992
   Google Scholar
• Gatarek D. Goldys B. On existence of optimal control for infinite - dimensional nonlinear stochastic systems preprint
   Google Scholar
• Gatarek , D. and Goldys , B. 1994 . On weak solutions of stochastic equations in Hilbert spaces , Stochastics and Stochastics Rep .
   Google Scholar
• Gatarek , D. and Goldys , B. On solving stochastic evolutions by the change of drift with application to optimal control . Proc. Stochastic P. D. Es and Applications . Edited by: Da Prato , G. and Tubaro , L. Pitman .
   Google Scholar
• Gatarek D. Goldys B. On invariant measures for diffusions on Banach spaces preprint
   Google Scholar
• Gatarek , D. and Sobczyk , J. 1994 . On the existence of optimal controls of Hilbert space-valued diffusions . SIAM J. Control Optimiz , 32 : 170 – 175 .
   Google Scholar
• Ichikawa , A. 1979 . Dynamic programming approach to stochastic evolution equations . SIAM J. Control Optimiz , 17 : 152 – 174 .
   Web of Science ®Google Scholar
• Kushner , H.J. 1978 . Optimality conditions for the average cost per unit time problem with a diffusion model . SIAM J. Control Optimiz , 16 : 330 – 346 .
   Web of Science ®Google Scholar
• Maslowski B. Seidler J. Ergodic properties of recurrent solutions of stochastic evolution equations preprint 81 1993 MU AV CR
   Google Scholar
• Peszat S. Zabczyk J. Strong Feller property and irreducibility for diffusions on Hilbert spaces Annals of Probability to appear
   Google Scholar
• Roxin , E. 1962 . The existence of optimal controls . Michigan Math. J , 9 : 109 – 119 .
   Google Scholar
• Stettner , L. 1986 . On the existence of an optimal per unit time control for a degenerate diffusion model . Bull. Polish Acad. Sci. Math , 34 : 749 – 769 .
   Google Scholar
• Tudor , C. 1989 . Optimal control of semilinear stochastic evolution equations . JAMO , 20 : 319 – 331 .
   Google Scholar
• Warga , J. 1972 . Optimal control of differential and functional equations , New York : Academic Press .
   Google Scholar
• Zhou , X.Y. 1992 . On the existence of optimal relaxed controls of stochastic partial differential equations . SIAM J. Control Optimiz , 30 : 247 – 261 .
   Google Scholar