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On stochastic relaxed control for partially observed diffusions

Published online by Cambridge University Press:  22 January 2016

W. H. Fleming  and
M. Nisio
W. H. Fleming
Affiliation:
Division of Applied Mathematics, Brown University, Prividence R. I., USA
M. Nisio
Affiliation:
Department of Mathematics, Kobe University, Rokko, Kobe 657, Japan
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In this paper we are concerned with stochastic relaxed control problems of the following kind. Let X(t), t ≥ 0, denote the state of a process being controlled, Y(t), t ≥ 0, the observation process and p(t, ·) a relaxed control, that is a process with values probability measures on the control region Г. The state and observation processes are governed by stochastic differential equations

and

where B and W are independent Brownian motions with values in Rn and Rm respectively, (put m = 1 for simplicity).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 93 , March 1984 , pp. 71 - 108
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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