Condition on the first short time interval. A jump contributes the generator term $Qf$, while local time grows at unit speed in the current coordinate and contributes $\partial_{\ell_i}f$. The <Markov property> and division by the interval length therefore give $\partial_tf_t=Mf_t$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 27K / a / Solution

 Solution (source code)