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

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 ${\partial }_t{f}_t=M{f}_t$.