Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

Jeremiah Birrell, Luc Rey-Bellet

Published 2018-12-12Version 1

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 non-parametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincar\'e, $\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds applicable to both discrete and continuous-time Markov processes. These bounds are well-behaved in the infinite-time limit and apply to steady-states.