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Strong bounds on perturbations

Author

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  • Bernd Heidergott
  • Arie Hordijk
  • Haralambie Leahu

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. Copyright The Author(s) 2009

Suggested Citation

  • Bernd Heidergott & Arie Hordijk & Haralambie Leahu, 2009. "Strong bounds on perturbations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 99-127, August.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:1:p:99-127
    DOI: 10.1007/s00186-008-0233-x
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    References listed on IDEAS

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    1. Louiza Bouallouche-Medjkoune & Djamil Aissani, 2006. "Performance analysis approximation in a queueing system of type M/G/1," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 341-356, May.
    2. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of all policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 421-448, December.
    3. Heidergott, B. & Leahu, H., 2008. "Differentiability of Product Measures," Serie Research Memoranda 0005, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Arie Hordijk & Alexander A. Yushkevich, 1999. "Blackwell optimality in the class of stationary policies in Markov decision chains with a Borel state space and unbounded rewards," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 1-39, March.
    5. Rommert Dekker & Arie Hordijk, 1988. "Average, Sensitive and Blackwell Optimal Policies in Denumerable Markov Decision Chains with Unbounded Rewards," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 395-420, August.
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    Cited by:

    1. Bernd Heidergott & Haralambie Leahu, 2010. "Weak Differentiability of Product Measures," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 27-51, February.

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