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In this paper we propose an efficient variance reduction approach foradditive functionals of Markov chains relying on a novel discrete timemartingale representation. Our approach is fully non-asymptotic and does notrequire the knowledge of the stationary distribution (and even any type ofergodicity) or specific structure of the underlying density. By rigorouslyanalyzing the convergence properties of the proposed algorithm, we show thatits cost-to-variance product is indeed smaller than one of the naive algorithm.The numerical performance of the new method is illustrated for theLangevin-type Markov Chain Monte Carlo (MCMC) methods.

Variance reduction for additive functional of Markov chains via martingale representations