We study weighted ensemble, an interacting particle method for sampling distributions of Markov chains that has been used in computational chemistry since the 1990s. Many important applications of weighted ensemble require the computation of long time averages. We establish the consistency of weighted ensemble in this setting by proving an ergodic theorem for time averages. As part of the proof, we derive explicit variance formulas that could be useful for optimizing the method.

翻译：我们研究加权共合物,这是自1990年代以来用于计算化学的Markov链取样分布的交互粒子方法。加权共合物的许多重要应用都需要计算较长时间的平均值。我们通过证明时间平均的离子定理来确定这一环境的加权共合物的一致性。作为证据的一部分,我们得出了可用于优化方法的明确差异公式。