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