2019/06/21 by Jeremiah Birrell, Markos A. Katsoulakis, Birrell, Jeremiah +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Energy · Mathematics · #60G40 #60J60 #62B10 #62F35 #91G20 #93E20 #Applied mathematics #Capital Investment and Risk Analysis #Climate Change Policy and Economics #Computer science #Energy, Environment, and Transportation Policies #Entropy (arrow of time) #Ergodic theory #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Kullback–Leibler divergence #Markov chain #Mathematical analysis #Mathematical optimization #Mathematics #Parametric statistics #Physics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical physics #Statistics #Stochastic processes and financial applications #Uncertainty quantification #cs.IT #math.IT #math.PR #msc:60G40 #msc:60J60 #msc:62B10 #msc:62F35 #msc:91G20 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1906.09282
35 pages, 10 figures
openalex publication_date 2019/06/21 · arxiv created 2020/09/02 · arxiv updated 2020/09/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Quantifying the impact of parametric and model-form uncertainty on the\npredictions of stochastic models is a key challenge in many applications.\nPrevious work has shown that the relative entropy rate is an effective tool for\nderiving path-space uncertainty quantification (UQ) bounds on ergodic averages.\nIn this work we identify appropriate information-theoretic objects for a wider\nrange of quantities of interest on path-space, such as hitting times and\nexponentially discounted observables, and develop the corresponding UQ bounds.\nIn addition, our method yields tighter UQ bounds, even in cases where previous\nrelative-entropy-based methods also apply, e.g., for ergodic averages. We\nillustrate these results with examples from option pricing, non-reversible\ndiffusion processes, stochastic control, semi-Markov queueing models, and\nexpectations and distributions of hitting times.\n