Section: New Results
Impulsive control for continuous-time Markov decision processes
The following result has been obtained by Alexey Piunovskiy and François Dufour (CQFD member).
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space
with both impulsive and continuous controls for the infinite-time horizon discounted cost.
The continuous-time controlled process is shown to be non explosive under appropriate hypotheses.
The so-called Bellman equation associated to this control problem is studied.
Sufficient conditions ensuring the existence and the uniqueness of a bounded measurable solution to this optimality equation are provided.
Moreover, it is shown that the value function of the optimization problem under consideration satisfies this optimality equation.
Sufficient conditions are also presented to ensure on one hand the existence of an optimal control strategy and on the other hand the existence of an