Working papers & books & topics

• Distances and metrics in probability theory
  Extended lecture notes with focus on (and complete proofs of) the relation of various metrics and distances appearing in probability theory (e.g. total variation, Chi-Squared, Kullback-Leibler / relative entropy, Hellinger, Prohorov, Levy, Kolmogorov, Wasserstein / bounded lipschitz, Ky Fan, ...). It is complemented by a unified approach to the Skorokhod metrics (J1, J2, M1, M2).
   
• Multivariance
  A new tool for estimating and detecting multivariate dependence. A series of papers is currently in preperation, including theoretic discussions, auxillary results, practical applications and an R-package.
   

Preprints / Submitted papers

• Notes on the interpretation of dependence measures -- Pearson's correlation, distance correlation, distance multicorrelations and their copula versions
  2020, arXiv
   
• On complex Gaussian random fields, Gaussian quadratic forms and sample distance multivariance
  (with G. Berschneider). 2018, v2:2019, arXiv
   
• Markovian Maximal Coupling of Markov Processes
  2016, arXiv
   
  

Books & Chapters

• Lévy-Type Processes: Construction, Approximation and Sample Path Properties
  (with R. Schilling and J. Wang). Series: Lecture Notes in Mathematics, Vol. 2099, Subseries: Lévy Matters, Springer, 2013. ISBN: 978-3-319-02684-1.
   
• Simulation of Brownian Motion
  Chapter in the Textbook: Brownian Motion - An Introduction to Stochastic Processes, R. Schilling, L. Partzsch, De Gruyter, 2012.
   

Papers

• Copula versions of distance multivariance and dHSIC via the distributional transform - a general approach to construct invariant dependence measures
  Statistics, 2020, 18 pages + online supplement, Online Article and arXiv
   
• Dependence and dependence structures: estimation and visualization using the unifying concept of distance multivariance
  Open Statistics, Vol. 1, No. 1 (2020) 1–46, ISSN (Online) 2657-3601, DOI:10.1515/stat-2020-0001, open access.
   
• Embedded Markov chain approximations in Skorokhod topologies
  Probability and Mathematical Statistics, Vol. 39, No. 2 (2019), 259-277, open access.
   
• Distance multivariance: New dependence measures for random vectors
  (with M. Keller-Ressel, R. Schilling). The Annals of Statistics, Vol. 47, No. 5 (2019) 2757-2789, open access.
  (To avoid confusion by changing titles, note that it is the published revised version of the preprint: Detecting independence of random vectors II. Distance multivariance and Gaussian multivariance arXiv.)
   
• Detecting independence of random vectors: generalized distance covariance and Gaussian covariance
  (with M. Keller-Ressel, R. Schilling). Modern Stochastics: Theory and Applications, Vol. 5, No. 3 (2018) 353-383, open access.
  (To avoid confusion by changing titles, note that it is the published revised version of the preprint: Detecting independence of random vectors I. Generalized distance covariance and Gaussian covariance. arXiv.)
   
• Über die Lebensdauer von Seifenblasen - eine Exponentialverteilung im Experiment?
  MNU Journal, No. 4 (2018) 239-241. PDF
   
• Feller Evolution Systems: Generators and Approximation
  Stochastics and Dynamics, Vol. 14, 1350025 (2014), Online Article, PDF - arxiv
   
• Feynman formulas and path integrals for some evolution semigroups related to τ-quantization
  (with Y. Butko, R. Schilling, O. Smolyanov). Russian Journal of Mathematical Physics, Vol. 18 (2011) 387-399.
   
• On the construction of Feller processes with unbounded coefficients
  Electronic Communications in Probability, Vol. 16 (2011) 545-555. Online Article
   
• The Euler scheme for Feller processes
  (with A. Schnurr). Stochastic Analysis and Applications, Vol. 29 (2011) 1045-1056.
   
• Convergence rate of numerical solutions to SFDEs with jumps
  (with J. Bao, X. Mao, C. Yuan). Journal of Computational and Applied Mathematics. Vol. 236, No. 2 (2011) 119-131. Online Article
   
• An Overshoot Approach to Recurrence and Transience of Markov Processes
  Stochastic Processes and their Applications. Vol. 121, No. 9 (2011) 1962–1981. Online Article
   
• Constructions of Coupling Processes for Lévy Processes
  (with R. Schilling, J. Wang). Stochastic Processes and their Applications Vol. 121, No. 6 (2011) 1201-1216. Online Article Extras
   
• Feller processes: The Next Generation in Modeling. Brownian Motion, Lévy processes and Beyond
  PLoS ONE 5(12): e15102 (2010). Online Article - PDF incl. source code
   
• Approximation of Feller processes by Markov chains with Lévy increments
  (with R. Schilling). Stochastics and Dynamics, Vol. 9, No. 1 (2009) 71–80. PDF
   
• Construction of time inhomogeneous Markov processes via evolution equations using pseudo-differential operators
  Journal of the London Mathematical Society (2) 78 (2008) 605–621. PDF
   
• The moderator effect that wasn’t there: Statistical problems in ambivalence research
  (with J. Ullrich, K. Schermelleh-Engel). Journal of Personality and Social Psychology 2008, Vol. 95, No. 4, 774–794.
   
• A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process
  Mathematische Nachrichten (278) 2005, 1235-1241.
   
• Remarks on Meixner-type Processes
  (with N. Jacob). In: Probabilistic Methods in Fluids (eds. I.M. Davies et al.) World Scientific Press (2003), 35-47.
  
   
• Some investigations on Feller processes generated by pseudo-differential operators
  PhD Thesis, University of Wales Swansea, 2004.
  
  

Software

• multivariance: Measuring Multivariate Dependence Using Distance Multivariance
  R-package. Initial release 2017 (Version 1.1.0, published 2018; last update: Version 2.3.0, 2020). Published on CRAN. To install use: install.packages("multivariance").

Letzte Änderung: 23.04.2020