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Stochastic maximum principle for optimal control of SPDEs. (English) Zbl 1256.93117
Summary: We show the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).
MSC:
93E20Optimal stochastic control (systems)
49K45Optimal stochastic control (optimality conditions)
60H15Stochastic partial differential equations
References:
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[3]Lu, Q.; Zhang, X.: General Pontryagin-type stochastic maximum principle and backward stochastic evolution equations in infinite dimensions, (2012)
[4]Lunardi, A.: Analytic semigroups and optimal regularity in parabolic problems, (1995)
[5]Peng, S.: A general stochastic maximum principle for optimal control problems, SIAM J. Control optim. 28, No. 4, 966-979 (1990) · Zbl 0712.93067 · doi:10.1137/0328054
[6]Tang, S. J.; Li, X. J.: Maximum principle for optimal control of distributed parameter stochastic systems with random jumps, Lecture notes in pure and appl. Math. 152, 867-890 (1994) · Zbl 0811.49021