Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g., for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times.
@article{arxiv.1906.09282,
title = {Quantification of Model Uncertainty on Path-Space via Goal-Oriented Relative Entropy},
author = {Jeremiah Birrell and Markos A. Katsoulakis and Luc Rey-Bellet},
journal= {arXiv preprint arXiv:1906.09282},
year = {2020}
}