Résumé
We consider a problem of change point detection for a continuous-time stochastic process in the family of piecewise deterministic Markov processes introduced by MHA Davis in the 80's. The process is only observed in discrete time and with noise, and the aim is to accurately detect the (random) time when its dynamics change and also select the new dynamics among a finite number of possibilities as soon as possible after the change-point. To do so, we turn the detection problem into an optimal stopping problem for partially observed Markov decision process with values in a continuous state space, and provide a discretization of the state space to be able to solve the problem numerically. Applications include for instance maintenance optimization where the change-point corresponds to a failure time of some equipment. Another application concerns treatment optimization for cancer patients. The change-point then corresponds to a sudden deterioration of the health of the patient. It must be detected early so that the treatment can be adapted.