We obtain criteria for exponential ergodicity and strong ergodicity of one-dimensional symmetric $\alpha$-stable jump diffusions, where $\alpha\in(1,2)$. Explicit lower bounds for the ergodic convergence rates are given based on the Green functions.
Ergodic convergence rates for time-changed symmetric Lévy processes in dimension one
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
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