Mathematics – Optimization and Control
Scientific paper
2012-04-15
Mathematics
Optimization and Control
56 pages
Scientific paper
The main purpose of this paper is to give a solution to a long-standing unsolved problem in stochastic control theory, i.e., to establish the Pontryagin-type maximum principle for optimal controls of infinite dimensional stochastic evolution equations with the control variable appeared in both the drift and the diffusion terms and with possibly nonconvex control domains. The key to do this is a correct formulation of operator-valued backward stochastic evolution equations (BSEEs for short), and how to define their solutions. General vector-valued BSEEs are studied as well. The solutions to both vector-valued and operator-valued BSEEs are defined in the sense of transposition, and the corresponding well-posedness results are presented.
Lü Qi
Zhang Xu
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