Martingale problem for a continuous-time Markov chain
= Martingale problem for a continuous-time Markov chain
A finite-state process has generator $Q$ exactly when, for every function $f$ on the state space,
$$
f(X_t)-f(X_0)-\int_0^t(Qf)(X_s)\,ds
$$
is a martingale with respect to the process filtration.