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Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations

Published online by Cambridge University Press:  22 January 2016

Makiko Nisio
Makiko Nisio*
Affiliation:
Department of Mathematics, Kobe University Rokko, Kobe 657, Japan
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Recently M. G. Crandall and P. L. Lions developed the viscosity theory on nonlinear equations in infinite dimensions and optimal control in Hilbert spaces, in two series of papers, [1], [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 13 - 37
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[ 1 ] Crandall, M. G. and Lions, P. L., Hamilton-Jacobi equations infinite dimensions, Part 1. J. Funct. Anal., 6, 2 (1985), 379–396. Part 2, 65 (1986), 368–405. Part 3, 68 (1986), 214–247. Part 4, 90 (1990), 273–283.Google Scholar
[ 2 ] Ikeda, N. and Watanabe, S., Stochastic Differential Equations and Diffusion Processes, Kodansha/North-Holland, Tokyo/Amsterdam, 1981.Google Scholar
[ 3 ] Krylov, N. V. and Rozovskii, B. L., On characteristics of the degenerate parabolic Ito equations of the second orders, Petrovskii Seminar, 8 (1982), 153–168 (in Russian).Google Scholar
[ 4 ] Lions, P. L., Viscosity solutions and optimal stochastic control in infinite dimensions, Part 1, Acta Math. 161 (1988), 243–278. Part 2, Lecture Notes in Math. 1390 (1988), 147–170. Part 3, J. Funct. Anal. 86 (1989), 1–18.Google Scholar
[ 5 ] Nagase, N. and Nisio, M., Optimal controls for stochastic partial differential equations, SIAM, J. Control Optim., 28 (1990), 186–213.Google Scholar
[ 6 ] Rochafellar, R. T., Convex analysis, Princeton Univ. Press, 1972.Google Scholar
[ 7 ] Rozovskii, B. L., Stochastic Evolution Systems, preprint.Google Scholar