Titlebook: General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in ; Qi Lü,Xu Zhang Book 2014 The Author(

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Working methods: from theory into practice,In this chapter, we prove a uniqueness result for transposition solutions to the operator-valued backward stochastic evolution Eq. (1.10) and a well-posedness result for transposition solutions to this equation for the special case that both the final datum and the nonhomogeneous term are valued in the Hilbert space of Hilbert-Schmidt operators.

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https://doi.org/10.1007/978-3-031-17084-3In this chapter, we study the well-posedness for the operator-valued backward stochastic evolution Eq. (1.10) with general final datum and nonhomogeneous term, in the sense of relaxed transposition solution.

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Integration into the community,In this chapter, we derive some regularity properties for the relaxed transposition solutions to the operator-valued backward stochastic evolution Eq. (1.10) with general final datum and nonhomogeneous term. These properties will play key roles in the proof of our general Pontryagin-type stochastic maximum principle, presented in Chap. 9.

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Community Pest Management in PracticeThe purpose of this chapter is to show a necessary condition for stochastic optimal controls when the control domain is a convex subset of some Hilbert space.

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Preliminaries,In this chapter, we present nine lemmas that will be used in the rest of this book. The first one is the classical Burkholder-Davis-Gundy inequality in infinite dimensions, while the rest are new technical results.

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Well-Posedness of the Operator-Valued BSEEs in the General Case,In this chapter, we study the well-posedness for the operator-valued backward stochastic evolution Eq. (1.10) with general final datum and nonhomogeneous term, in the sense of relaxed transposition solution.

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Some Properties of the Relaxed Transposition Solutions to the Operator-Valued BSEEs,In this chapter, we derive some regularity properties for the relaxed transposition solutions to the operator-valued backward stochastic evolution Eq. (1.10) with general final datum and nonhomogeneous term. These properties will play key roles in the proof of our general Pontryagin-type stochastic maximum principle, presented in Chap. 9.