14 citations · 52 across the 19 of their papers we have counts for
28 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…
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…
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…
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…
From Markov Processes to Semimartingales
Sebastian Rickelhoff, Alexander Schnurr
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, i…
On the rôle of singular functions in extending the probabilistic symbol to its most general class
Sebastian Rickelhoff, Alexander Schnurr
The probabilistic symbol is the right-hand side derivative of the characteristic functions corresponding to the one-dimensional marginals of a stochastic process. This object, as l…
Ordinal Pattern Dependence in the Context of Long-Range Dependence
Ines Nüßgen, Alexander Schnurr
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal infor…
Ordinal pattern dependence as a multivariate dependence measure
Annika Betken, Herold Dehling, Nüßgen +1
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of de…
Operator-stable-like Processes
Peter Scheffler, Alexander Schnurr, Daniel Schulte
In the present paper, we introduce so-called operator-stable-like processes. Roughly speaking, they behave locally like operator-stable processes, but they need not to be homogenou…
Ordinal Patterns in Long-Range Dependent Time Series
Annika Betken, Jannis Buchsteiner, Herold Dehling +3
We analyze the ordinal structure of long-range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points…
Ordinal Patterns in Clusters of Subsequent Extremes of Regularly Varying Time Series
Marco Oesting, Alexander Schnurr
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clust…
The Fourth Characteristic of a Semimartingale
Alexander Schnurr
We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space R^d. In particular Markov processes related…
Criteria for the Finiteness of the Strong -Variation for Lévy-type Processes
Martynas Manstavicius, Alexander Schnurr
Using generalized Blumenthal--Getoor indices, we obtain criteria for the finiteness of the -variation of Lévy-type processes. This class of stochastic processes includes solutio…
Laplace Symbols and Invariant Distributions
Anita Behme, Alexander Schnurr
We introduce a new kind of symbol in the framework of Itô processes which are bounded on one side. The connection between this symbol and the infinitesimal generator is analyzed. B…
Time Change Equations for Lévy Type Processes
Paul Krühner, Alexander Schnurr
In this paper we analyse time change equations (TCEs) for Lévy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial va…
Comparison of time-inhomogeneous Markov processes
Ludger Rueschendorf, Alexander Schnurr, Viktor Wolf
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two process…
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…
Testing for Structural Breaks via Ordinal Pattern Dependence
Alexander Schnurr, Herold Dehling
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Henc…
Generalization of the Blumenthal-Getoor index to the class of homogeneous diffusions with jumps and some applications
Alexander Schnurr
We introduce the probabilistic symbol for the class of homogeneous diffusions with jumps (in the sense of Jacod/Shiryaev). This concept generalizes the well-known characteristic ex…
A criterion for invariant measures of Itô processes based on the symbol
Anita Behme, Alexander Schnurr
An integral criterion for the existence of an invariant measure of an Itô process is developed. This new criterion is based on the probabilistic symbol of the Itô process. In contr…
COGARCH: Symbol, Generator and Characteristics
Alexander Schnurr
We describe the technique how to use the symbol in order to calculate the generator and the characteristics of an Itô process. As an example we analyze the COGARCH process which is…
On Deterministic Markov Processes: Expandability and Related Topics
Alexander Schnurr
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria…
SDEs Driven by SDE Solutions
Alexander Schnurr
We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SD…
Well-balanced Levy Driven Ornstein-Uhlenbeck Processes
Alexander Schnurr, Jeannette H. C. Woerner
In this paper we introduce the well-balanced Lévy driven Ornstein-Uhlenbeck process as a moving average process of the form . In contrast to Lévy driven…