5 papers
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…
A Comparison of Different Representations of Ordinal Patterns and Their Usability in Data Analysis
Alexander Schnurr, Angelika Silbernagel
We describe and analyze different approaches to represent ordinal patterns. All of these can be found in the literature. The most important representations (plus sub-classes) are c…
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…
The Time-Dependent Symbol of a Non-Homogeneous Itô Process and corresponding Maximal Inequalities
Sebastian Rickelhoff, Alexander Schnurr
The probabilistic symbol is defined as the right-hand side derivative at time zero of the characteristic functions corresponding to the one-dimensional marginals of a time-homogene…
An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series
Alexander Schnurr
We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non…