34 citations · 146 across the 12 of their papers we have counts for
12 papers
Notes on the interpretation of dependence measures
Björn Böttcher
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to…
On complex Gaussian random fields, Gaussian quadratic forms and sample distance multivariance
Georg Berschneider, Björn Böttcher
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we…
Dependence and dependence structures: estimation and visualization using the unifying concept of distance multivariance
Björn Böttcher
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension…
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance
Björn Böttcher, Martin Keller-Ressel, René L. Schilling
Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Székely, Rizzo and Bakirov can be e…
Distance multivariance: New dependence measures for random vectors
Björn Böttcher, Martin Keller-Ressel, René L. Schilling
We introduce two new measures for the dependence of random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^…
Markovian Maximal Coupling of Markov Processes
Björn Böttcher
Markovian maximal couplings of Markov processes are characterized by an equality of total variation and a distance of Wasserstein type. If a Markovian maximal coupling is a Feller…
Embedded Markov chain approximations in Skorokhod topologies
Björn Böttcher
In order to approximate a continuous time stochastic process by discrete time Markov chains one has several options to embed the Markov chains into continuous time processes. On th…
Feller Evolution Systems: Generators and Approximation
Björn Böttcher
A time and space inhomogeneous Markov process is a Feller evolution process, if the corresponding evolution system on the continuous functions vanishing at infinity is strongly con…
Constructions of Coupling Processes for Lévy Processes
Björn Böttcher, René L. Schilling, Jian Wang
We construct optimal Markov couplings of Lévy processes, whose Lévy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Br…
Feller Processes: The Next Generation in Modeling. Brownian Motion, Lévy Processes and Beyond
Björn Böttcher
We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space depend…
An Overshoot Approach to Recurrence and Transience of Markov Processes
Björn Böttcher
We develop criteria for recurrence and transience of one-dimensional Markov processes which have jumps and oscillate between and . The conditions are based on a…
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…