An LP approach to dynamic programming principles for stochastic control problems with state constraints |
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| Institution: | 1. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France;2. Universitatea Transilvania, Facultatea de Matematica-Informatica, Str. Iuliu Maniu nr. 50, Brasov, Romania;3. Université de Perpignan, 52 av. Paul Alduy, 66000 Perpignan, France;1. Department of Chemistry, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 04763, Republic of Korea;2. Theoretical Physics and Applied Mathematics Department, Ural Federal University, Mira Street 19, 620002 Yekaterinburg, Russia;3. Department of Physics and Engineering Physics, University of Saskatchewan, 116 Science Place, Saskatoon, Canada;4. M.N. Mikheev Institute of Metal Physics, Russian Academy of Sciences-Ural Division, 620990 Yekaterinburg, Russia;5. Institute of Physics and Technology, Ural Federal University, 9 Mira Street, 620002 Yekaterinburg, Russia;6. Center for Integrated Nanostructure Physics, Institute for Basic Science, Sungkyunkwan University, Suwon 440-746, Republic of Korea;7. Department of Physics and Department of Energy Science, Sungkyunkwan University, Suwon 440-746, Republic of Korea;1. Department of Physics, Faculty of Science, Gazi University, 06500 Ankara, Turkey;2. Photonics Application and Research Center, Gazi University, 06500 Ankara, Turkey;1. Department of Physics, Jamia Millia Islamia (Central University), New Delhi, India;2. Centre for Nanoscience and Nanotechnology, Jamia Millia Islamia (Central University), New Delhi, India |
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| Abstract: | We study a class of nonlinear stochastic control problems with semicontinuous cost and state constraints using a linear programming (LP) approach. First, we provide a primal linearized problem stated on an appropriate space of probability measures with support contained in the set of constraints. This space is completely characterized by the coefficients of the control system. Second, we prove a semigroup property for this set of probability measures appearing in the definition of the primal value function. This leads to dynamic programming principles for control problems under state constraints with general (bounded) costs. A further linearized DPP is obtained for lower semicontinuous costs. |
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