Photo from academic.microsoft.com
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… Click to show full 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:
mean minkowski;
homogeneous random;
minkowski content;
content homogeneous;
random fractals
Journal Title: Mathematics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Mathematics
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!