Abstract
This paper provides strong bounds on perturbations over a collection of independent random variables, where ‘strong’ has to be understood as uniform w.r.t. some functional norm. Our analysis is based on studying the concept of weak differentiability. By applying a fundamental result from the theory of Banach spaces, we show that weak differentiability implies norm Lipschitz continuity. This result leads to bounds on the sensitivity of finite products of probability measures, in norm sense. We apply our results to derive bounds on perturbations for the transient waiting times in a G/G/1 queue.
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This research is supported by the Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Heidergott, B., Hordijk, A. & Leahu, H. Strong bounds on perturbations. Math Meth Oper Res 70, 99–127 (2009). https://doi.org/10.1007/s00186-008-0233-x
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DOI: https://doi.org/10.1007/s00186-008-0233-x