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math.PR2024
Fixing a Minor Mistake in the Theory of Stochastic Integration and Differential Equations
Sebastian Rickelhoff, Alexander Schnurr
When considering stochastic integration and the theory of stochastic differential equations, P. Protter's textbook \cite{protter} undoubtedly is a main piece of standard literature…
stat.AP2024
Generalized Ordinal Patterns Allowing for Ties and Their Applications in Hydrology
Alexander Schnurr, Svenja Fischer
When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow…
math.ST2024
Depth Patterns and their Applications in Animal Tracking
Annika Betken, Alexander Schnurr
We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we ar…