  We consider the estimation of the characteristic exponent of the input to a
L\'evy-driven storage model. The input process is not directly observed, but
rather the workload process is sampled on an equispaced grid. 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, the
distribution of the estimation errors is asymptotically normal for a high
frequency sampling scheme. A resampling scheme that uses the available
information in a more efficient manner is suggested and studied via simulation
experiments.
