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On the Bellman equations with varying control

Published online by Cambridge University Press:  17 April 2009

Shigeaki Koike
Shigeaki Koike
Affiliation:
Department of Mathematics, Saitama University, Urawa, Saitama 338, Japan, e-mail: [email protected]
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The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 51 - 62
Copyright
Copyright © Australian Mathematical Society 1996

References

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