Obituary
Hans-Peter Scheffler was born on April 4, 1965 in Siegen, where he also graduated with a degree in mathematics in 1990. He then spent more than a decade at the University of Dortmund, where he completed his doctorate in 1992 under Prof. Hazod and habilitated in 1998. After substitute professorships at the University of Dortmund and the University of Siegen, he was appointed to the University of Nevada, Reno (USA) in 2004, where he spent two years. In 2006, he returned to his home town of Siegen and took up a professorship in stochastics. Since then, his workplace has been at the university's Emmy Noether Campus - in the very building of the former Jung Stilling Hospital where he was once born. He leaves behind his wife and a daughter, to whom we extend our deepest sympathy.
We bid farewell to an internationally leading representative of probability theory, who leaves behind an extensive body of work on multivariate limit theorems and operator-self-similar stochastic processes and random fields. An extremely fruitful collaboration with Mark Meerschaert (University of Nevada, later Michigan State University) began during his doctoral phase. This collaboration resulted in numerous joint publications in scientific journals as well as the highly acclaimed monograph "Limit Distributions for Sums of Independent Random Vectors". The two were not only linked by a long-standing scientific partnership, in which they complemented each other in an almost ideal way, but also by a deep personal friendship.
With his extraordinary commitment to teaching, research and academic self-administration, Hans-Peter Scheffler has rendered lasting services to the University of Siegen. The Department of Mathematics mourns the loss of a world-renowned researcher and popular lecturer, while the staff mourn the loss of a valuable and amusing colleague who was always something special.
In Hans-Peter Scheffler, we have lost a long-standing friend and academic companion who enriched us not only with his professional brilliance, but also with his unconventional manner, his humor and his warmth. We will miss his joyful "Huhu!" in the morning, his tongue-in-cheek comments such as "The semester is dragging on!" in the very first week of lectures. We will remember him with gratitude and perhaps stir our coffee with our finger in his memory. If you would like to commemorate him in a less painful way, you are welcome to put on "The Unforgiven" by Metallica as an alternative.
(by Peter Kern and Alfred Müller)
Publications by Hans-Peter Scheffler
- Portfolio Modeling With Heavy Tailed Random Vectors
(with Mark M. Meerschaert).
In: Handbook of Heavy Tailed Distributions in Finance (Svetlozar T. Rachev, 2003), Chapter 15, 595-640. - Nonparametric Methods for Heavy Tailed Vector Data: A Survey With Applications From Finance and Hydrology
(with Mark M. Meerschaert).
In: Recent Advances and Trends in Nonparametric Statistics (Michael G. Akritas and Dimitris N. Politis, 2003), 265-279. - Lagrangian Characterization of Contaminant Transport Through Multidimensional Heterogeneous Media With Limited Heterogeneity Information (with Zhang Yong, David A. Benson, Eric M. LaBolle and Mark M. Meerschaert).
In: Conference Proceedings for MODFLOW and MORE 2006: Managing Ground-Water Systems, International Ground Water Modeling Center (Eileen P. Poeter, Chunmiao Zheng and Mary C. Hill, 2006), 639-643. - Efficient Simulations of Stable Random Fields and Its Applications (with Wolfgang Karcher and Evgeny Spodarev).
In: Stereology and Image Analysis: ECS10, 10th European Congress of ISS (Vincenzo Capasso, Giacomo Aletti and Alessandra Micheletti, 2009), 63-72. - Continuous Time Random Walks and Space-Time Fractional Differential Equations
(with Mark M. Meerschaert).
In: Handbook of Fractional Calculus with Applications, Volume 1: Basic Theory (Anatoly Kochubei and Yuri Luchko, 2019), 385-406.
- The Domains of Partial Attraction of Probabilities on Groups and on Vector Spaces
(with Wilfried Hazod, 1991).
Journal of Theoretical Probability, 6, 175-186. - Domains of Attraction of Stable Measures on the Heisenberg Group
(1993).
Probability and Mathematical Statistics, 14(2), 327-345. - D-Domains of Attraction of Stable Measures on Stratified Lie Groups
(1994).
Journal of Theoretical Probability, 7, 767-792. - Domains of Semi-Stable Attraction of Nonnormal Semi-Stable Laws
(1994).
Journal of Multivariate Analysis, 51(2), 432-444. - Moments of Measures Attracted to Operator Semi-Stable Laws
(1995).
Statistics and Probability Letters, 24(3), 187-192. - The "Two Series Theorem" for Symmetric Random Variables on Nilpotent Lie Groups
(with Daniel Neuenschwander, 1995).
Publicationes Mathematicae Debrecen, 47(1-2), 173-179. - A Law of the Iterated Logarithm for Stable Laws on Homogeneous Groups
(1995).
Publicationes Mathematicae Debrecen, 47(3-4), 377-391. - Laws of the Iterated Logarithm for the Central Part of (Semi-)Stable Measures on the Heisenberg Groups
(with Daniel Neuenschwander, 1996).
Monatshefte für Mathematik, 121(3), 265-274. - Generalized Domains of Semistable Attraction of Nonnormal Laws
(with Mark M. Meerschaert, 1996).
Journal of Applied Analysis, 2(2), 203-215. - Series Representations for Semistable Laws and Their Domains of Semistable Attraction
(with Mark M. Meerschaert, 1996).
Journal of Theoretical Probability, 9, 931-959. - Large Deviations and Law of the Iterated Logarithm for Generalized Domains of Attraction
(1997).
Probability and Mathematical Statistics, 17(1), 65-77. - The Structure of Generalized Domains of Semistable Attraction
(with Mark M. Meerschaert, 1997).
Statistics and Probability Letters, 33(4), 367-372. - Spectral Decomposition for Generalized Domains of Semistable Attraction
(with Mark M. Meerschaert, 1997).
Journal of Theoretical Probability, 10, 51-71. - A Law of the Iterated Logarithm for Semistable Laws on Vector Spaces and Homogeneous Groups
(1998).
Journal of Mathematical Sciences, 89(5), 1545-1552. - Convergence of Semitypes
(with Mark M. Meerschaert, 1998).
Publicationes Mathematicae Debrecen, 53(1-2), 119-131. - A Simple Robust Estimation Method for the Thickness of Heavy Tails
(with Mark M. Meerschaert, 1998).
Journal of Statistical Planning and Inference, 71(1-2), 19-34. - Normalizers of Compact Subgroups, the Existence of Commuting Automorphisms and Applications to Operator Semistable Measures
(with Wilfried Hazod, Karl Heinrich Hofmann, Michael Wüstner and Hansmartin Zeuner, 1998).
Journal of Lie Theory, 8(2), 189-209. - Series Representation for Operator Semistable Laws and Domains of Normal Attraction
(1998).
Journal of Mathematical Sciences, 92(4), 4062-4084. - Domains of Attraction on Sturm-Liouville Hypergroups of Polynomial Growth
(with Hansmartin Zeuner, 1999).
Journal of Applied Analysis, 5(2), 153-170. - Sample Covariance Matrix for Random Vectors With Heavy Tails
(with Mark M. Meerschaert, 1999).
Journal of Theoretical Probability, 12, 821-838. - Moment Estimator for Random Vectors With Heavy Tails
(with Mark M. Meerschaert, 1999).
Journal of Multivariate Analysis, 71(1), 145-159. - On Estimation of the Spectral Measure of Certain Nonnormal Operator Stable Laws
(1999).
Statistics and Probability Letters, 43(4), 385-392. - Multivariable Regular Variation of Functions and Measures
(with Mark M. Meerschaert, 1999).
Journal of Applied Analysis, 5(1), 125-146. - One-Dimensional Marginals of Operator Stable Laws and Their Domains of Attraction
(with Mark M. Meerschaert, 1999).
Publicationes Mathematicae Debrecen, 55(3-4), 487-499. - Spectral Decomposition for Operator Self-Similar Processes and Their Generalized Domains of Attraction
(with Mark M. Meerschaert, 1999).
Stochastic Processes and Their Applications, 84(1), 71-80. - Strongly τ-Decomposable and Selfdecomposable Laws on Simply Connected Nilpotent Lie Groups
(with Wilfried Hazod, 1999).
Monatshefte der Mathematik, 128(4), 269-282. - Moving Averages of Random Vectors With Regularly Varying Tails
(with Mark M. Meerschaert, 2000).
Journal of Time Series Analysis, 21(3), 297-328. - Limit Laws for Symmetric k-Tensors of Regularly Varying Measures
(with Mark M. Meerschaert, 2000).
Journal of Multivariate Analysis, 73(2), 241-261. - Multivariate R-O Varying Measures. Part I: Uniform Bounds
(2000).
Proceedings of the London Mathematical Society, 81(1), 231-256. - A Law of the Iterated Logarithm for Heavy Tailed Random Vectors
(2000).
Probability Theory and Related Fields, 116(2), 257-271. - A Law of the Iterated Logarithm for Randomly Stopped Sums of Heavy Tailed Random Vectors
(with Peter Becker-Kern, 2000).
Monatshefte der Mathematik, 130(4), 329-347. - Norming Operators for Generalized Domains of Semistable Attraction
(2001).
Publicationes Mathematicae Debrecen, 58(3), 391-409. - Sample Cross-Correlations for Moving Averages With Regularly Varying Tails
(with Mark M. Meerschaert, 2001).
Journal of Time Series Analysis, 22(4), 481-492. - Multivariate R-O Varying Measures. Part II: Individual Bounds
(2002).
Journal of Mathematical Sciences, 111(6), 3868-3878. - Semistable Lévy Motion (with Mark M. Meerschaert, 2002).
Fractional Calculus and Applied Analysis, 5(1), 27-54. - Stochastic Solution of Space-Time Fractional Diffusion Equations
(with Mark M. Meerschaert, David A. Benson and Boris Baeumer, 2002).
Physical Review E, 65, 041103. - Governing Equations and Solutions of Anomalous Random Walk Limits
(with Mark M. Meerschaert, David A. Benson and Peter Becker-Kern, 2002).
Physical Review E, 66, 060102. - Hausdorff Dimension of Operator Stable Sample Path
(with Peter Becker-Kern and Mark M. Meerschaert, 2003).
Monatshefte der Mathematik, 140(2), 91-101. - Precise Asymptotics in Spitzer's and Baum-Katz Law of Large Numbers: The Semistable Case
(2003).
Journal of Mathematical Analysis and Applications, 288(1), 285-298. - The Operator ν-Stable Laws
(with Tomasz J. Kozubowski and Mark M. Meerschaert, 2004).
Publicationes Mathematicae Debrecen, 63(4), 569-585. - Limit Theorems for Coupled Continuous Time Random Walks
(with Peter Becker-Kern and Mark M. Meerschaert, 2004).
Annals of Probability, 32(1B), 730-756. - A Limit Theorem for Continuous Time Random Walks With Two Time Scales
(with Peter Becker-Kern and Mark M. Meerschaert, 2004).
Journal of Applied Probability, 41(2), 455-466. - Limit Theorems for Continuous Time Random Walks With Infinite Mean Waiting Times
(with Mark M. Meerschaert, 2004).
Journal of Applied Probability, 41(3), 623-638. - On Multiple-Particle Continuous Time Random Walks
(with Peter Becker-Kern, 2004).
Journal of Applied Mathematics, 2004(3), 213-233. - Limiting Behavior of Weighted Sums of Heavy-Tailed Random Vectors and Applications
(with Chen Pingyan, 2004).
Probability and Mathematical Statistics, 24(2), 281-295. - Vector Grünwald Formula for Fractional Derivatives (with Mark M. Meerschaert and Jeff Mortensen, 2004).
Journal of Fractional Calculus and Applied Analysis, 7(1), 61-81. - Operator Geometric Stable Laws
(with Tomasz J. Kozubowski, Mark M. Meerschaert and Anna K. Panorska, 2005).
Journal of Multivariate Analysis, 92(2), 298-323. - Limit Theorems for Continuous Time Random Walks With Slowly Varying Waiting Times
(with Mark M. Meerschaert, 2005).
Statistics and Probability Letters, 71(1), 15-22. - Limiting Behavior of Weighted Sums of Heavy-Tailed Random Vectors
(with Chen Pingyan, 2005).
Publicationes Mathematicae Debrecen, 66, 137-151. - How to Find Stability in a Purely Semistable Context
(with Peter Becker-Kern, 2005).
Yokohama Mathematical Journal, 51(2), 75-88. - Finite Difference Methods for Two-Dimensional Fractional Dispersion Equation
(with Mark M. Meerschaert and Charles Tadjeran, 2005).
Journal of Computational Physics, 211(1), 249-261. - A Second-Order Accurate Numerical Approximation for the Fractional Diffusion Equation
(with Charles Tadjeran and Mark M. Meerschaert, 2005).
Journal of Computational Physics, 213(1), 205-213. - On Using Random Walks to Solve the Space-Fractional Advection-Dispersion Equations
(with Zhang Yong, David A. Benson and Mark M. Meerschaert, 2006).
Journal of Statistical Physics, 123, 89-110. - Stochastic Model for Ultraslow Diffusion
(with Mark M. Meerschaert, 2006).
Stochastic Processes and Their Applications, 116(9), 1215-1235. - Aquifer Operator-Scaling and the Effect on Solute Mixing and Dispersion
(with David A. Benson, Mark M. Meerschaert and Boris Baeumer, 2006).
Water Resources Research, 42(1), 1-18. - Random Walk Approximation of Fractional-Order Multiscaling Anomalous Diffusion
(with Yong Zhang, David A. Benson, Mark M. Meerschaert and Eric M. LaBolle, 2006).
Physical Review E, 74, 026706. - Operator Scaling Stable Random Fields
(with Hermine Biermé and Mark M. Meerschaert, 2007).
Stochastic Processes and Their Applications, 117(3), 312-332. - Fourier Series Approximation of Linear Fractional Stable Motion
(with Hermine Biermé, 2008).
Journal of Fourier Analysis and Applications, 14, 180-202. - Triangular Array Limits for Continuous Time Random Walks
(with Mark M. Meerschaert, 2008).
Stochastic Processes and Their Applications, 118(9), 1606-1633. - Transport of Conservative Solutes in Simulated Fracture Networks 2. Ensemble Solute Transport and the Correspondence to Operator-Stable Limit Distributions
(with Donald M. Reeves, David A. Benson and Mark M. Meerschaert, 2008).
Water Resources Research, 44(5), W05410. - Cluster Continuous Time Random Walks
(with Agnieszka Jurlewicz and Mark M. Meerschaert, 2011).
Studia Mathematica, 205(1), 13-30. - Multi-Operator Scaling Random Fields
(with Hermine Biermé and Céline Lacaux, 2011).
Stochastic Processes and Their Applications, 121(11), 2642-2677. - Application of Operator-Scaling Anisotropic Random Fields to Binary Mixtures
(with Denis Anders, Alexander Hoffmann and Kerstin Weinberg, 2011).
Philosophical Magazine, 91(29), 3766-3792. - Clustered Continuous-Time Random Walks: Diffusion and Relaxation Consequences
(with Karina Weron, Aleksander Stanislavsky, Agnieszka Jurlewicz and Mark M. Meerschaert, 2012).
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2142), 1615-1628. - Fractional Governing Equations for Coupled Random Walks
(with Agnieszka Jurlewicz, Peter Kern and Mark M. Meerschaert, 2012).
Computers and Mathematics With Applications, 64(10), 3021-3036. - Tauberian Theorems for Matrix Regular Variation
(with Mark M. Meerschaert, 2013).
Transactions of the American Mathematical Society, 365(4), 2207-2221. - Simulation of Infinitely Divisible Random Fields
(with Wolfgang Karcher and Evgeny Spodarev, 2013).
Communications in Statistics: Simulation and Computation, 42(1), 215-246. - Extreme Value Theory With Operator Norming
(with Mark M. Meerschaert and Stilian A. Stoev, 2013).
Extremes, 16(4), 407-428. - Parameter Estimation for Operator Scaling Random Fields
(with Chae Y. Lim and Mark M. Meerschaert, 2014).
Journal of Multivariate Analysis, 123, 172-183. - Limit Theorems and Governing Equations for Lévy Walks
(with Marcin Magdziarz, Peter Straka and Piotr Żebrowski, 2015).
Stochastic Processes and Their Applications, 125(11), 4021-4038. - Applications of Inverse Tempered Stable Subordinators
(with Mahmoud S. Alrawashdeh, James F. Kelly and Mark M. Meerschaert, 2017).
Computers and Mathematics With Applications, 73(6), 892-905. - Implicit Extremes and Implicit Max-Stable Laws
(with Stilian A. Stoev, 2017).
Extremes, 20(2), 265-299. - On Joint Sum/Max Stability and Sum/Max Domains of Attraction
(with Katharina Hees, 2018).
Probability and Mathematical Statistics, 38(1), 157-189. - Coupled Continuous Time Random Maxima
(with Katharina Hees, 2018).
Extremes, 21(2), 235-259. - Operator-Stable and Operator-Self-Similar Random Fields
(with Dustin Kremer, 2019).
Stochastic Processes and Their Applications, 129(10), 4082-4107. - Multi Operator-Stable Random Measures and Fields
(with Dustin Kremer, 2019).
Stochastic Models, 35(4), 429-468. - Theory of Generalized Discrepancies on a Ball of Arbitrary Finite Dimensions and Algorithms for Finding Low-Discrepancy Point Sets
(with Amna Ishtiaq and Volker Michel, 2019).
GEM - International Journal on Geomathematics, 10, 21. - Multivariate Stochastic Integrals With Respect to Independently Scattered Random Measures on δ-Rings
(with Dustin Kremer, 2019).
Publicationes Mathematicae Debrecen, 95(1-2), 39-66. - About atomless random measures on δ-rings
(with Dustin Kremer, 2020).
Statistics and Probability Letters, 164, 108805. - Multivariate Tempered Stable Random Fields
(with Dustin Kremer, 2021).
Journal of Mathematical Analysis and Applications, 503(2), 125347. - Operator-Stable-Like Processes
(with Alexander Schnurr and Daniel Schulte, 2023).
Stochastic Analysis and Applications, 41(2), 185-213. - Semistable Distributions as Marginals of Operator Stable Laws
(with Peter Kern, 2025).
Statistics and Probability Letters, 226, 110458.
Monograph:
Limit Distributions for Sums of Independent Random Vectors
The monograph, written in collaboration with Mark M. Meerschaert, was published by Wiley in 2001. It contains an introduction to the theory of central limit theorems and the latest (at the time of publication) research results in this field.
Supervised theses
- Alexander Hoffmann (2011) - Operator Scaling Stable Random Sheets With Application to Binary Mixtures
- Tobias Kegel (2011) - Simulation and Estimation of Operator Scaling Stable Random Fields
- Anissa Bouk Ali (2014) - Tempered operator stable distributions
- Katharina Hees (2014) - Joint Convergence of Sum and Maximum and the Limit Behavior of Coupled Continuous Time Random Maxima
- Johannes Goldbach (2016) - A New Approach to Multivariate Extreme Value Theory: f-Implicit Max-Infinitely Divisible Distributions and f-Implicit Max-Stable Processes
- Dustin Kremer (2017) - Multivariate Stochastic Integrals with Application to the Example of Operator-Stable and Operator-Self-Similar Random Fields
- Daniel Schulte (2018) - On operator-stable-like processes and their properties
- Andreas Stahl (2019) - Tempered Operator Scaling Stable Random Fields
Workshop in memory of Prof. Dr. Hans-Peter Scheffler
On September 23, 2025, the 6th workshop "Stochastics and Analysis Düsseldorf-Siegen" (short: StAnDS) took place in memory of Hans-Peter Scheffler at the Emmy-Noether-Campus of the University of Siegen. The workshop, which is regularly organized with colleagues from Heinrich Heine University Düsseldorf, was initiated by Hans-Peter Scheffler in 2015.
| Time of day | Lecture |
|---|---|
| 13:30 - 14:00 | Alexander Schnurr (University of Siegen) Dependence Analysis Using Ordinal Patterns With Ties |
| 14:00 - 14:30 | Marco Oesting (University of Stuttgart) Central Limit Theory for Peaks-Over-Threshold Partial Sums of Long Memory Linear Time Series |
| 14:30 - 15:00 | Daniel Curkovic (HHU Düsseldorf) Normal Approximation on Product Spaces via p-Poincaré Inequalities |
| 15:00 - 15:30 | Nils Detering (HHU Düsseldorf) Too big to fail? What random networks tell us about financial crises |
| 15:30 - 16:00 | Coffee break |
| 16:00 - 17:00 | Peter Kern (HHU Düsseldorf) & Alfred Müller (University of Siegen) The life and work of Hans-Peter Scheffler |
