Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms

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Bernstein's inequalities for general Markov chains (2018, unknown): “Recall that, for any function f ∈ L 02 , its asymptotic variance is given by By Rosenthal (2003, Proposition 1), for any h ∈ L 02 , Let Z = ( I − P + Π ) − 1 − Π be the negative of the reduced resolvent of P with respect to its largest eigenvalue 1.”
A spectral analytic comparison of trace-class data augmentation algorithms and their sandwich variants (2011, background): “, Rosenthal (2003), page 170]. If P satisfies additional regularity conditions, much more can be said about the convergence of the corresponding Markov chain. Assume that the operator P is compact and positive, and let {αi} denote its eigenvalues, all of which reside in [0,1). The number of eigenval”