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Maximum principle of optimal control problem for Markov process. (Chinese) Zbl 0723.93082

For a Markov type stochastic system with Bolza type cost functional and with the target set being a relative convex body of finite co-dimension in \(L^ 2(\Omega,{\mathcal F}_ T,P,{\mathbb{R}}^ n)\), the author proves Pontryagin type maximum principle for optimal controls. In the discussed problem, the control domain \(\Gamma\) is an arbitrary nonempty set in \({\mathbb{R}}^ m\), the diffusion coefficient \(\sigma\) (t,x) is allowed to be degenerate, but is independent of control v yet. The main tool used is the vector measure theory.

MSC:

93E20 Optimal stochastic control
60J99 Markov processes
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