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Input estimation from discrete workload observations in a Lévy-driven storage system
Dennis Nieman, Michel Mandjes, Liron Ravner · 2022-05-20 · via math.ST updates on arXiv.org

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.

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