Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

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 (Poincare, 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.