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Error bounds for computing the expectation by Markov chain Monte Carlo. (English) Zbl 1208.65009

The error of reversible Markov chain Monte Carlo methods is studied for approximating the expectation of a function. Explicit error bounds with respect to the \(l_2\)-, \(l_4\)- and \(l_\infty\)-norm of the function are proven. By the estimation the well-known asymptotical limit of the error is attained, i.e. given bounds are correct to first order as \(n \to \infty\). The dependence of the error on a burn-in of the Markov chain is discussed. Very complete, a detailed approach to the subject. An excellent work.

MSC:

65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
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