Controllability of semilinear stochastic evolution equations in Hilbert space

Journal of Applied Mathematics and Stochastic Analysis

Volumn 14, Issue 4, 2002, Pages 329-339

  Balasubramaniam, P ^a   Dauer, J P ^b  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

^b UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

Author keywords

Banach Fixed Point Theorem; Controllability; Stochastic Evolution Equation; Wiener Process

Indexed keywords

EID: 0348115294     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953301000296     Document Type: Article

References (23)

1. Ahmed, N.U., Stability of limit measures induced by stochastic differential equations on Hilbert space, Comput. Math. Appl. 22 (1991), 41-48.
2. Ahmed, N.U. and Ding, X., A semilinear McKean-Vlasov stochastic evolution equation in Hilbert space, Stoch. Proc. Appl. 60 (1995), 65-85.
3. Anichini, G., Controllability of nonlinear control process with prescribed controls, J. Optim. Theory Appl. 32 (1980), 183-199.
4. Astrom, K.J., Introduction to Stochastic Control Theory, Academic Press, New York 1970.
5. Balachandran, K., Dauer, J.P. and Balasubramaniam, P., Controllability of nonlinear integrodifferential systems in Banach space, J. Optim. Theory Appl. 84 (1995), 83-91.
6. Bellman, R., Jacquez, J. and Kalaba, R., Some mathematical aspect of Chemotherapy. I: One-organ models, Bull. Math. Biophys. 22 (1960), 181-198.
7. Dauer, J.P., Controllability of nonlinear systems with restrained controls, J. Optim. Theory Appl. 14 (1974), 251-262.
8. Dauer, J.P. and Balasubramaniam, P., Null controllability of semilinear integro-differential system in Banach space, Appl. Math. Lett. 10 (1997), 117-123.
9. Dauer, J.P., Balachandran, K. and Balasubramaniam, P., Asymptotic null controllability of nonlinear perturbed systems, J. Optim. Theory Appl. 83 (1994), 167-179.
10. Dawson, D.A., Critical dynamics and fluctuations for a mean-field model of cooperative behavior, J. Statist. Phys. 31 (1983), 29-85.
11. Dawson, D.A. and Gärtner, J., Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics 20 (1987), 247-308.
12. Fuhrman, M., Smoothing properties of nonlinear stochastic equations in Hilbert spaces, Nonl. Diff. Eqns. Appl. 3 (1996), 445-464.
13. Funaki, T., A certain class of diffusion processes associated with nonlinear parabolic equations, Probab. Theory Related Fields 67 (1984), 331-348.
14. Ichickawa, A., Stability of semilinear stochastic evolution equations, J. Math. Anal. Appl. 90 (1982), 12-44.
15. Jousis, J.C. and Wexler, D., On exact controllability in Hubert spaces, J. Diff. Eqns. 49 (1983), 258-269.
16. Leonard, C., Large deviations and law of large numbers for mean field type interacting particle system, Stoch. Process. Appl. 25 (1987), 215-235.
17. Liu, K., On stability for a class of semilinear stochastic evolution equations, Stoch. Proc. Appl. 70 (1997), 219-241.
18. McKean, H.P., A class of Markov processes associated with nonlinear parabolic equations, Proc. NAS 56 (1966), 1907-1911.
19. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York 1983.
20. Rabah, R. and Karakchou, J., Exact controllability and complete stabilizability for linear systems in Hubert spaces, Appl. Math. Lett. 10 (1997), 35-40.
21. Tsokos, C.P. and Padgett, W.J., Random Integral Equations with Application to Life Sciences and Engineering, Academic Press, New York 1974.
22. Wonham, V.M., Random Differential Equations in Control Theory, Prob. Meth. in Appl. Math. Vol. 2, Academic Press, New York 1970.
23. Zabczyk, J., Controllability of stochastic linear systems, stochastic differential systems, In: Lecture Notes in Control and Information Sciences, Springer Verlag, New York 43 (1982), 144-154.