Abstract
We consider a time-average estimator fk of a functional of a Markov chain. Under a coupling assumption, we show that the expectation of fk has a limit μ as the number of time steps goes to infinity. We describe a modification of fk that yields an unbiased estimator [Formula: see text] of μ. It is shown that [Formula: see text] is square integrable and has finite expected running time. Under certain conditions, [Formula: see text] can be built without any precomputations and is asymptotically at least as efficient as fk , up to a multiplicative constant arbitrarily close to one. Our approach also provides an unbiased estimator for the bias of fk . We study applications to volatility forecasting, queues, and the simulation of high-dimensional Gaussian vectors. Our numerical experiments are consistent with our theoretical findings.
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