Un théorème de représentation des solutions de viscosité d'une équation d'Hamilton-Jacobi-Bellman ergodique dégénérée sur le tore

We consider an ergodic Hamilton-Jacobi-Bellman equation coming from a stochastic control problem in which there are exactly k points where the dynamics vanishes and the Lagrangian is minimal. Under a stabilizability assumption, we state that the solutions of the ergodic equation are uniquely determined by their value on these k points, and that the set of solutions is sup-norm isometric to a non-empty closed convex set whose dimension is less or equal to k. To cite this article: M. Akian et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).