We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct applications, explicit sufficient conditions for exponential and strong ergodicity are given. Some examples are also presented.
Ergodic convergence rates of Markov processes--eigenvalues, inequalities and ergodic theory
Convergence Rates in Strong Ergodicity by Hitting Times and $L^2$-exponential Convergence Rates
Ergodicity and Convergence Rates for Stable Jump Diffusions
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