On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

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Publisher
Springer-Verlag
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9132-2
Publisher site
See Article on Publisher Site

Abstract

In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2011

References

  • Generalized solutions in nonlinear stochastic control problems
    Dufour, F.; Miller, B.M.

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