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For a stationary moving average random field, a non-parametric low frequencyestimator of the L\'evy density of its infinitely divisible independentlyscattered integrator measure is given. The plug-in estimate is based on thesolution $w$ of the linear integral equation $v(x) = \int_{\mathbb{R}^d} g(s)w(h(s)x)ds$, where $g,h:\mathbb{R}^d \rightarrow \mathbb{R}$ are givenmeasurable functions and $v$ is a (weighted) $L^2$-function on $\mathbb{R}$. Weinvestigate conditions for the existence and uniqueness of this solution andgive $L^2$-error bounds for the resulting estimates. An application to purejump moving averages and a simulation study round off the paper.

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