Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-16T23:58:38.223Z Has data issue: false hasContentIssue false
  • English
  • Français

On the existence of optimal control for controlled stochastic partial differential equations

Published online by Cambridge University Press:  22 January 2016

Noriaki Nagase
Noriaki Nagase*
Affiliation:
Department of Mathematics and System Fundamentals, Division of System Science, Kobe University, Rokko, Kobe, 657, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we are concerned with stochastic control problems of the following kind. Let Y(t) be a d’-dimensional Brownian motion defined on a probability space (Ω, F, Ft, P) and u(t) an admissible control. We consider the Cauchy problem of stochastic partial differential equations (SPDE in short)

where L(y, u) is the 2nd order elliptic differential operator and M(y) the 1st order differential operator.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 73 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[1] Bensoussan, A., Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions, Stochastics, 9 (1983), 169–222.CrossRefGoogle Scholar
[2] Fleming, W. H. and Pardoux, E., Optimal control for partially observed diffusions, SIAM J. Control Optim., 20 (1982), 261–285.Google Scholar
[3] Ikeda, N. and Watanabe, S., Stochastic Differential Equations and Diffusion Processes, Kodansha/North-Holland, Tokyo/Amsterdam, 1981.Google Scholar
[4] Krylov, N. V. and Rozovskii, B. L., On the Cauchy problem for stochastic partial differential equations, Math. USSR-Izv., 11 (1977), 1267–1284.CrossRefGoogle Scholar
[5] Krylov, N. V. and Rozovskii, B. L., On the conditional distributions of diffusion processes, Math. USSR-Izv., 12 (1978), 336–356.Google Scholar
[6] Lions, J. L., Equations Différentielles Opérationnelles et Problèmes aux Limites, Springer-Verlag, Berlin, 1961.Google Scholar
[7] Pardoux, E., Stochastic partial differential equations and filtering of diffusion processes, Stochastics, 3 (1979), 127–167.Google Scholar
[8] Rozovskii, B. L., Nonnegative L 1-solutions of second order stochastic parabolic equations with random coefficients, Transl. Math. Eng., (1985), 410–427.Google Scholar
[9] Rozovskii, B. L. and Shimizu, A., Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density, Nagoya Math. J., 84 (1981), 195–208.CrossRefGoogle Scholar