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An LP Approach to Dynamic Programming Principles for Stochastic Control Problems with State Constraints

Dan Goreac 1 Carina Ivascu Oana Silvia Serea 2
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
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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https://hal-upec-upem.archives-ouvertes.fr/hal-00747715
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Submitted on : Thursday, November 1, 2012 - 12:08:44 PM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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Dan Goreac, Carina Ivascu, Oana Silvia Serea. An LP Approach to Dynamic Programming Principles for Stochastic Control Problems with State Constraints. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2013, 77 (-), pp.59-73. ⟨10.1016/j.na.2012.09.002⟩. ⟨hal-00747715⟩

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