Seminario de Probabilidad y Procesos Estocásticos

Resumen:

This talk addresses the ergodic optimal control problem for a success-runs Markov chain. We first characterize the set of steady state-control pairs, identifying a meaningful subclass of uniform (normal) steady states. We then analyze dissipativity by deriving a closed-form storage function, linking the chain to the stability of the associated deterministic difference equation that governs the state distribution. The long-run average reward problem is solved explicitly, showing that the optimal policy is a stationary normal steady state independent of the initial condition. Finally, we demonstrate the framework’s applicability through two examples: a connection to a class of mean-field optimal control problems and a solution to the optimal management of even-aged forest systems.