  The computable convergence rates in strong ergodicity for Markov processes
are obtained by using uniformly bounded moments of hitting times and the
convergence rates in $L^2$-exponential ergodicity. We reveal a phenomenon for a
class of Markov processes which are strongly ergodic that the two convergence
rates in both strong ergodicity and exponential ergodicity are identical. These
processes vary from Markov chains, diffusions to SDEs driven by symmetric
stable processes.
