Abstract
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).
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