14 citations · 52 across the 19 of their papers we have counts for
19 papers · 1 filter
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…
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…
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…
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…
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…
On the Semimartingale Nature of Feller Processes with Killing
Alexander Schnurr
Let U be an open set in R^d. We show that under a mild assumption on the richness of the generator a Feller process in U with (predictable) killing is a semimartingale. To this end…
A Classification of Deterministic Hunt Processes with Some Applications
Alexander Schnurr
Deterministic processes form an important building block of several classes of processes. We provide a method to classify deterministic Hunt processes. Within this framework we cha…
The Symbol Associated with the Solution of a Stochastic Differential Equation
Rene L. Schilling, Alexander Schnurr
We consider a stochastic differential equations which is driven by a Levy process. It turns out that the solution process is a Feller process if the coefficient of the SDE is bound…
The Euler scheme for Feller processes
Björn Böttcher, Alexander Schnurr
We consider the Euler scheme for stochastic differential equations with jumps, whose intensity might be infinite and the jump structure may depend on the position. This general typ…