46 citations · 149 across the 14 of their papers we have counts for
5 papers · 1 filter
Mean Lipschitz-Killing curvatures for homogeneous random fractals
Jan Rataj, Steffen Winter, Martina Zähle
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider…
Mean Euler characteristic of stationary random closed sets
Jan Rataj
The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observat…
Dilation volumes of sets of finite perimeter
Markus Kiderlen, Jan Rataj
This paper analyzes the first order behavior (that is, the right sided derivative) of the volume of the dilation as converges to zero. Here and are subsets…
Random sets of finite perimeter
Jan Rataj
An approach to modelling random sets with locally finite perimeter as random elements in the corresponding subspace of functions is suggested. A Crofton formula for flat sect…
Approximations of the Wiener sausage and its curvature measures
Jan Rataj, Evgeny Spodarev, Daniel Meschenmoser
A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random pol…