@article{Hofstadler2025, author = {Hofstadler, Julian}, title = {Optimal convergence rates of MCMC integration for functions with unbounded second moment}, series = {Journal of Applied Probability}, volume = {62 (2025)}, journal = {Journal of Applied Probability}, number = {3}, publisher = {Cambridge University Press}, address = {Cambridge}, doi = {10.1017/jpr.2024.108}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-19310}, pages = {1069 -- 1075}, year = {2025}, abstract = {We study the Markov chain Monte Carlo estimator for numerical integration for func- tions that do not need to be square integrable with respect to the invariant distribution. For chains with a spectral gap we show that the absolute mean error for L^p functions, with p ∈ (1, 2), decreases like n^(1/p)-1 , which is known to be the optimal rate. This improves currently known results where an additional parameter δ > 0 appears and the convergence is of order n^((1+δ)/p)-1 .}, language = {en} }