We start with a standard Markov process $X$ and a continuous additive process $A$ of $X$ with fine support $\Phi$. We form the time changed process $X_\tau$, and we compute its weak infinitesimal generator in terms of the weak infinitesimal generator of the process $X$ and of the Levy system of $(X_\tau, \tau)$. We give some examples.
"Infinitesimal Generators of Time Changed Processes." Ann. Probab. 8 (4) 716 - 726, August, 1980. https://doi.org/10.1214/aop/1176994661