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Transposition method for backward stochastic evolution equations revisited, and its application. (English) Zbl 1316.93126

Summary: The main purpose of this paper is to improve our transposition method to solve both vector-valued and operator-valued backward stochastic evolution equations with a general filtration. As its application, we obtain a general Pontryagin-type maximum principle for optimal controls of stochastic evolution equations in infinite dimensions. We also establish a Pontryagin-type maximum principle for a stochastic linear quadratic problems.

MSC:

93E20 Optimal stochastic control
93C25 Control/observation systems in abstract spaces
49K45 Optimality conditions for problems involving randomness
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