Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

Abstract

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 (Poincar{é}, $\log$-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.

37 pages

References in corpus (2)

• A Relative Entropy Rate Method for Path Space Sensitivity Analysis of Stationary Complex Stochastic Dynamics
• Scalable Information Inequalities for Uncertainty Quantification