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Operator-valued backward stochastic Lyapunov equations in infinite dimensions, and its application. (English) Zbl 1405.93233

Summary: We establish the well-posedness of operator-valued backward stochastic Lyapunov equations in infinite dimensions, in the sense of \(V\)-transposition solution and of relaxed transposition solution. As an application, we obtain a Pontryagin-type maximum principle for the optimal control of controlled stochastic evolution equations.

MSC:

93E20 Optimal stochastic control
93C15 Control/observation systems governed by ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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