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Input estimation from discrete workload observations in a Lévy-driven storage system

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Listed:
  • Nieman, Dennis
  • Mandjes, Michel
  • Ravner, Liron

Abstract

Our goal is to estimate the characteristic exponent of the input to a Lévy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the Laplace-Stieltjes transform of the workload at exponentially distributed sampling times. The estimator is pointwise consistent for any observation grid. Moreover, a high frequency sampling scheme yields asymptotically normal estimation errors for a class of input processes. A resampling scheme that uses the available information in a more efficient manner is suggested and assessed via simulation experiments.

Suggested Citation

  • Nieman, Dennis & Mandjes, Michel & Ravner, Liron, 2025. "Input estimation from discrete workload observations in a Lévy-driven storage system," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002190
    DOI: 10.1016/j.spl.2024.110250
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    References listed on IDEAS

    as
    1. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 314-328, August.
    2. Mandjes, M. & Ravner, L., 2021. "Hypothesis testing for a Lévy-driven storage system by Poisson sampling," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 41-73.
    3. Kappus, Johanna & Reiß, Markus, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers 2010-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.
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