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We consider the estimation of the characteristic exponent of the input to aL\'evy-driven storage model. The input process is not directly observed, butrather the workload process is sampled on an equispaced grid. The estimatorrelies on an approximate moment equation associated with the Laplace-Stieltjestransform of the workload at exponentially distributed sampling times. Theestimator is pointwise consistent for any observation grid. Moreover, thedistribution of the estimation errors is asymptotically normal for a highfrequency sampling scheme. A resampling scheme that uses the availableinformation in a more efficient manner is suggested and studied via simulationexperiments.

Input estimation from discrete workload observations in a L\'evy-driven storage system