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

07/05/2018

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by   Jochen Glück, et al.

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For given measurable functions g,h:R^d →R and a (weighted) L^2-function v on R we study existence and uniqueness of a solution w to the integral equation v(x) = ∫_R^d g(s) w(h(s)x)ds. Such integral equations arise in the study of infinitely divisible moving average random fields. As a consequence of our solution theory to the aforementioned equation, we can thus derive non-parametric estimators for the Lévy density of the underlying random measure.