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by Xun Yu Zhou, Jiongmin Yong, Xunjing Li
http://epubs.siam.org/sam-bin/getfile/SICON/articles/27997.ps.Z
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Abstract:
Abstract. This paper studies controlled systems governed by Ito's stochastic di#erential equations in which control variables are allowed to enter both drift and di#usion terms. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. This theorem is shown to have wider applicability than the restrictive classical verification theorems, which require the associated dynamic programming equations to have smooth solutions. Based on the new verification result, optimal stochastic feedback controls are obtained by maximizing the generalized Hamiltonians over both the control regions and the superdi#erentials of the value functions. Key words. stochastic optimal control, verification theorem, Hamilton--Jacobi--Bellman equation, viscosity solution, superdi#erential, feedback control
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