Estimate the exponential convergence rate of f-ergodicity via spectral gap

This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, reversible chain, it proved that of holds if only spectral gap generator positive. Moreover, equal to gap. For irreversible case, positivity remains a sufficient condition f-ergodicity. The effectiveness these results are illustrated by some typical examples.