Rudolf, DanielDanielRudolf2023-03-312023-03-312010https://resolver.sub.uni-goettingen.de/purl?gro-2/123638We study the error of reversible Markov chain Monte Carlo methods for approx-imating the expectation of a function. Explicit error bounds with respect to thel2-,l4-andl1-norm of the function are proven. By the estimation the well-known asymptotical limitof the error is attained, i.e. our bounds are correct to first order asn!1. We discuss thedependence of the error on a burn-in of the Markov chain. Furthermore we suggest andjustify a specific burn-in for optimizing the algorithm.enjournal_article10.1515/mcma.2010.012