Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 356 / 3 / a / Solution

The pair $(X_t,V_t)$ is a hybrid-state process: position is continuous and velocity is discrete. It is Markov because its future law is fixed by the present position and velocity. Position $X_t$ alone is generally non-Markovian, since its future displacement depends on the hidden persistent velocity.