7 citations · 18 across the 15 of their papers we have counts for
5 papers · 1 filter
On approximation theorems for the Euler characteristic with applications to the bootstrap
Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the…
On the law of the iterated logarithm and strong invariance principles in stochastic geometry
Johannes Krebs
We study the law of the iterated logarithm (Khinchin (1924), Kolmogorov (1929)) and related strong invariance principles in stochastic geometry. As potential applications, we think…
On limit theorems for persistent Betti numbers from dependent data
Johannes Krebs
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descript…
On the asymptotic normality of persistent Betti numbers
Johannes Krebs, Wolfgang Polonik
Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Be…
Consistency and Asymptotic Normality of Stochastic Euler Schemes for Ordinary Differential Equations
Johannes T. N. Krebs
General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these p…