Adv. Math. Econ. Volume 6, pp.1-38 (2004)

On the fiber product of Young measures with application to a control problem with measures

Charles Castaing1, Paul Raynaud de Fitte2
1 Département de Mathématiques, Case 051, Université Montpellier II, 34095 Montpellier cedex 5, France
2 Laboratoire Raphaëel Salem, UMR CNRS 6085, UFR Sciences, Université de Rouen, 76821 Mont Saint Aignan Cedex, France
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This paper studies, in the context of separable metric spaces, the stable convergence of the fiber product for Young measures with applications to a control problem governed by an ordinary differential equations where the controls are Young measures. Essentially we study some variational properties of the value functions and the existence of quasi-saddle points of these functions which occurs in this dynamic control problem, and also their link with the viscosity solution of the associated Hamilton--Jacobi--Bellman equation.
Key Words:
Young measure, relaxed control, fiber product, dynamic programming, viscosity solution