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arXiv · 1506.07342

Inhomogeneous refinement equations with random affine maps

Rafał Kapica·Janusz Morawiec
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Abstract

Given a probability space $(Ω,{\mathcal A},P)$, random variables $L,M\colonΩ\to\mathbb R$ and $g\in L^1(\mathbb R)$ we obtain two characterizations of these $f\in L^1(\mathbb R)$ which are solutions of the inhomogeneous refinement equation with a random affine map of the form $f(x)=\int_Ω|L(ω)|f(L(ω)x-M(ω))P(dω)+g(x)$.

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Rafał Kapica, Janusz Morawiec. 2015-06-24. Inhomogeneous refinement equations with random affine maps. https://doi.org/10.1080/10236198.2015.1065823

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