  We consider a change-point detection problem for a simple class of Piecewise
Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in
discrete time and through noise, and the aim is to propose a numerical method
to accurately detect both the date of the change of dynamics and the new regime
after the change. To do so, we state the problem as an optimal stopping problem
for a partially observed discrete-time Markov decision process taking values in
a continuous state space and provide a discretization of the state space based
on quantization to approximate the value function and build a tractable
stopping policy. We provide error bounds for the approximation of the value
function and numerical simulations to assess the performance of our candidate
policy.
