Ergodicity and the generator.

Question

For a markov process $X_t$ adapted to ${\cal F}_t$, let $A$ satisfy $$\lim_{h\longrightarrow 0}[E\{f(X_{t+h})|{\cal F}_t\}-f(X_t)]/h = Af(X_t).$$ What are (references to?) conditions that allow one to conclude that $$\lim_{T\longrightarrow\infty}\frac{1}{T}\int_0^TAf(X_t)dt\;=\;0.$$ Thanks!