A solution to a linear integral equation with an application to statistics of infinitely divisible moving averages

For a stationary moving average random field, a nonparametric low frequency estimator of the Lévy density of its infinitely divisible independently scattered integrator measure is given. The plug‐in estimate is based on the solution w of the linear integral equation v ( x ) = ∫ℝ dg ( s ) w ( h ( s ) x ) d s , where g , h : ℝ d → ℝ are given measurable functions and v is a (weighted)L 2‐function on ℝ . We investigate conditions for the existence and uniqueness of this solution and giveL 2‐error bounds for the resulting estimates. An application to pure jump moving averages and a simulation study round off the paper.