Weak convergence rates of Markov transition kernels imply variance convergence bounds for Lipschitz functions and chi-squared divergence bounds under reversibility with Lipschitz initial densities.
Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré.Journal of Functional Analysis254727–759
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Implications of weak convergence rates of Markov transition kernels
Weak convergence rates of Markov transition kernels imply variance convergence bounds for Lipschitz functions and chi-squared divergence bounds under reversibility with Lipschitz initial densities.