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Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities

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 Added by Jeremiah Birrell
 Publication date 2018
  fields
and research's language is English




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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{e}, $log$-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.



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171 - J.-R. Chazottes , F. Redig 2010
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