Convergence Rates in Strong Ergodicity by Hitting Times and $L^2$-exponential Convergence Rates

Yong-Hua Mao, Tao Wang

Published 2021-02-14Version 1

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.