The Mean Minkowski Content of Homogeneous Random Fractals

Martina Zähle
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Martina Zähle: Institute of Mathematics, University of Jena, D-07743 Jena, Germany

Mathematics, 2020, vol. 8, issue 6, 1-13

Abstract: Homogeneous random fractals form a probabilistic generalisation of self-similar sets with more dependencies than in random recursive constructions. Under the Uniform Strong Open Set Condition we show that the mean D -dimensional (average) Minkowski content is positive and finite, where the mean Minkowski dimension D is, in general, greater than its almost sure variant. Moreover, an integral representation extending that from the special deterministic case is derived.

Keywords: fractals; random homogeneous constructions; code trees; mean Minkowski content (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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