In this paper we propose an efficient variance reduction approach for additive functionals of Markov chains relying on a novel discrete time martingale representation. Our approach is fully non-asymptotic and does not require the knowledge of the stationary distribution (and even any type of ergodicity) or specific structure of the underlying density. By rigorously analyzing the convergence properties of the proposed algorithm, we show that its cost-to-variance product is indeed smaller than one of the naive algorithm. The numerical performance of the new method is illustrated for the Langevin-type Markov Chain Monte Carlo (MCMC) methods.

翻译：在本文中,我们建议对Markov链链的添加功能采取有效的减少差异办法,依靠一种新的离散时间表示法。我们的办法完全不无谓,不需要了解固定分布(甚至任何类型的电子分配)或潜在密度的具体结构。我们通过严格分析提议的算法的趋同特性,表明其成本到差价产品确实小于一种天真算法。新的方法的数字性能为Langevin-type Markov链条蒙特卡洛(MCMC)方法作了说明。