SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 2, Page 539-572, January 2020.
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e., robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincaré, $\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds for time-averaged observables, comparing a Markov process to a second (not necessarily Markov) process. These bounds are well behaved in the infinite-time limit and apply to steady-states of both discrete and continuous-time Markov processes.

中文翻译：

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通过变分原理和泛函不等式对马尔可夫过程的不确定性量化

SIAM / ASA不确定性量化杂志，第8卷，第2期，第539-572页，2020年1月。
事实证明，基于信息论的变分原理可以有效地为存在数量的目标量提供可扩展的不确定性量化（即稳健性）界限。非参数模型形式的不确定性。在这项工作中，我们将这种变分公式与函数不等式（庞加莱，$ \ log $ -Sobolev，Liapunov函数）结合起来，得出时间平均可观测量的明确不确定性量化范围，将马尔可夫过程与第二个（不一定是马尔可夫）过程进行比较。这些界限在无限时限内表现良好，适用于离散和连续时间马尔可夫过程的稳态。