Preprints / Publications
Prof. Dr. Hans-Peter Scheffler
Fachbereich Mathematik
Universität Siegen
Veröffentlichungen
Stand: Dezember 2013
Dissertation und Habilitationsschrift
- Anziehungsbereiche stabiler Wahrscheinlichkeitsmaße auf stratifizierbaren Lie–Gruppen, Dissertation, Universität Dortmund (1992).
- Multivariable R-O variation and generalized domains of semistable attraction, Habilitationsschrift, Universität Dortmund (1997).
Veröffentlichungen in referierten Zeitschriften
- The domains of partial attraction of probabilities on groups and on vector spaces, Journal of Theoretical Probability, Vol 6 (1991), pp. 175–186 (mit Wilfried Hazod, Fachbereich Mathematik, Universität Dortmund).
- Domains of attraction of stable measures on the Heisenberg group, Probability and Mathematical Statistic, Vol. 14 (1993), pp. 327–345
- –domains of attraction of stable measures on stratified Lie groups, Journal of Theoretical Probability, Vol 7 (1994), pp. 767–792.
- Domains of semi–stable attraction of nonnormal semi–stable laws, Journal of Multivariate Analysis, Vol. 51 (1994), pp. 432–444.
- Moments of measures attracted to operator semi–stable laws, Statistics and Probability Letters, Vol. 24 (1995), pp. 187–192.
- A law of the iterated logarithm for stable laws on stratified Lie groups, Publicationes Mathematicae Debrecen, Vol. 47 (1995), pp. 377–391.
- The ”two series theorem” for symmetric random variables on nilpotent Lie groups, Publicationes Mathematicae Debrecen Vol. 47 (1995), pp. 173–179. (mit Daniel Neuenschwander).
- Laws of the iterated logarithm for the central part of (semi-)stable measures on the Heisenberg groups, Monatshefte für Mathematik, Vol. 121 (1996), pp. 265–274, (mit Daniel Neuenschwander, Ingenieurschule Biel, Biel).
- Generalized domains of semistable attraction of nonnormal laws, Journal Applied Analysis Vol. 2 (1996), pp. 203–215 ,(mit Mark Meerschaert, Department of Mathematics, University of Nevada, Reno).
- Series representations for semistable laws and their domains of semistable attraction, Journal of Theoretical Probability Vol. 9 (1996), pp. 931–959, (mit Mark Meerschaert).
- Large deviations and law of the iterated logarithm for generalized domains of attraction, Probability and Mathematical Statistics, Vol. 17 (1997), pp. 65–77.
- The structure of generalized domains of semistable attraction, Statistics and Probability Letters Vol. 33 (1997), pp. 367–372, (mit Mark Meerschaert).
- Spectral decomposition for generalized domains of semistable attraction, Journal of Theoretical Probability Vol. 10 (1997), pp. 51–71, (mit Mark Meerschaert).
- A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups, J. Math. Sciences., Vol. 89 (5) (1998), pp. 1545–1552.
- Convergence of semitypes, Publicationes Mathematicae Debrecen Vol. 53 (1998), pp. 119–131, (mit Mark Meerschaert).
- A simple robust estimator for the thickness of heavy tails, Journal of Statistical Planning and Inference Vol. 71 (1998), pp. 19–34, (mit Mark Meerschaert).
- Normalizers of compact subgroups, the existence of commuting automorphisms and applications to operator semistable measures, Journal of Lie Theory Vol. 8 (1998), pp. 189–209, (mit W. Hazod, Fachbereich Mathematik, Universität Dortmund, Hm. Zeuner, Fachbereich Mathematik, Universität Dortmund und K.H. Hoffmann und M. Wüstner, Fachbereich Mathematik, Universität Karlsruhe).
- Domains of attraction on Sturm Liouville Hypergroups of polynomial growth, J. Applied Analysis Vol. 5 (1999), pp. 153–170 (mit Hansmartin Zeuner, Fachbereich Mathematik, Universität Dortmund).
- Sample covariance matrix for random vectors with heavy tails, J. Theoretical Probab. Vol. 12, pp. 821–838, (1999), (mit Mark Meerschaert).
- Moment estimator for random vectors with heavy tails, J. Multivariate Anal. Vol. 71, pp. 145–159 (1999), (mit Mark Meerschaert).
- Series representation for operator semistable laws and domains of normal attraction, J. Math. Science Vol. 92 (4) (1999) pp. 4062–4084.
- On estimation of the spectral measure of certain nonnormal operator stable laws, Statistics and Probability Letters Vol. 43, 385–392 (1999).
- Multivariable Regular Variation of Functions and Measures, Journal Applied Analysis Vol. 5, pp. 125–146 (1999), (mit Mark Meerschaert).
- One-dimensional marginals of operator stable laws and their domains of attraction, Publ. Math. Debrecen Vol. 55, pp. 487–499 (1999), (mit Mark Meerschaert).
- Spectral decomposition for operator self-similar processes and their generalized domains of attraction, Stoch. Proc. Appl. Vol. 84 (1999), pp. 71–80 (mit Mark Meerschaert).
- Strongly τ-decomposable and selfdecomposable laws on simply connected nilpotent Lie groups, Monatshefte Math. Vol. 128, pp. 269–282 (1999), (mit W. Hazod).
- Moving averages of random vectors with regularly varying tails, J. Time Series Anal. Vol. 21 (3), pp. 297–328 (2000) (mit Mark Meerschaert).
- Limit laws for symmetric k-tensors of regularly varying measures, J. Multivariate Anal. Vol. 73, pp. 241–261 (2000), (mit Mark Meerschaert).
- Multivariate R-O varying measures. Part I: Uniform bounds, Proc. London Math. Soc. Vol. 81 (3) (2000), pp. 231–256.
- A law of the iterated logarithm for heavy tailed random vectors, Prob. Theory Related Fields Vol. 116 (2000), pp. 257–271.
- A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors, Monatshefte Math. Vol.130 (2000), pp. 329–347 (mit P. Becker-Kern, Universität Dortmund).
- Norming operators for generalized domains of semistable attraction, Publ. Math. Debrecen Vol. 58, pp. 391–409 (2001).
- Sample cross-correlations for moving averages with regularly varying tails, J. Time Series Anal. Vol. 22 (4), pp. 481–492 (2001), (mit Mark Meerschaert).
- Multivariate R-O varying measures. Part II: Individual bounds, J. Math. Science. Vol. 111 (6) (2002), pp. 3868–3878.
- Semistable Lévy Motion, Fractional Calculus and Applied Analysis Vol. 5 (2002), pp. 27–54 (mit M. Meerschaert).
- Stochastic solution of space-time fractional diffusion equations, Physical Review E Vol. 65 (2002), (mit M. Meerschaert, D.A. Beson, Desert Research Institute, Reno, Nevada and Boris Baeumer, Department of Mathematics and Statistics, University of Otago, New Zealand).
- Governing equations and solutions of anomalous random walk limits, Physical Review E Vol. 66 (6) (mit M.Meerschaert, D. Benson und P. Becker-Kern) (2002).
- Hausdorff Dimension of operator stable sample path, Monatshefte Mathematik Vol. 140, 91–101 (2003), (mit M. Meerschaert und P. Becker-Kern).
- Precise Asymptotics in Spitzer’s and Baum-Katz Law of Large Numbers: The semistable case, J. Math. Anal. Appl. Vol. 288, 285–298, (2003).
- The Operator ν-stable laws, Publ. Math. Deberecen Vol. 63 (4), 569–585, (mit T.J. Kozubowski, University of Nevada, Reno und M. Meerschaert) (2004).
- Limit Theorems for Coupled Continuous Time Random Walks, Annals Probab. Vol. 32, 730–756 (mit P. Becker-Kern und M.Meerschaert) (2004).
- A limit theorem for continuous time random walks with two time scales, J. Appl. Probab. Vol. 41, 455–466 (2004), (mit P. Becker-Kern und M. Meerschaert).
- Limit theorems for continuous time random walks with infinite mean waiting times, J Appl. Probab. Vol. 41, 623–638 (2004), (mit M. Meerschaert).
- On multiple particle continuous time random walks, J. Appl. Math. Vol. 2004:3, 213–233 (2004), (mit P. Becker-Kern).
- Limiting Behavior of Weighted Sums of Heavy-tailed Random Vectors and Applications, Probab. Math. Stat. Vol. 24, 281–295, (2004) (mit Chen Pingyan)
- Vector Grünwald formula for fractional derivatives, J. Fractional Calculus and Applied Analysis, Vol. 7, 61–81 (2004), (mit Mark Meerschaert und Jeff Mortensen, Department of Mathematics, University of Nevada, Reno).
- Operator geometric stable laws, J. Multivariate Anal. Vol. 92, 298–232 (mit M. Meerschaert, T.J. Kozubowski and A.K. Panorska, University of Nevada, Reno) (2005).
- Limit theorems for continuous time random walks with slowly varying waiting times, Stoch. Probab. Letters Vol. 71, 15–22 (2005), (mit M. Meerschaert).
- Limiting behavior of weighted sums of heavy-tailed random vectors, Publ. Math. Debrecen, Vol. 66, 137–151 (2005), (mit Chen Pingyan, Dept. of Math., Jinan University, Guangzhou, P.R. China).
- How to find stability in a purely semistable context, Yokohama Mathematical Journal, Vol. 51, 75–88, (2005), (mit P. Becker-Kern).
- Finite difference methods for two-dimensional fractional dispersion equation, J. Comput. Phys. Vol. 211, 249–261 (2005), (mit M. Meerschaert und Charles Tadjeran, Department of Mathematics and Statistics, University of Nevada, Reno).
- A second order accurate numerical approximation for the fractional diffusion equation, J. Comput. Phys. Vol. 213, 205–213 (2005), (mit M. Meerschaert und Charles Tadjeran).
- On using random walks to solve the space-fractional advection-dispersion equations, J. Statistical Physics Vol. 123, 89–110 (2006), (mit Zhang, Yong and D.A. Benson, Department of Geology, Colorado School of Mines and M. Meerschaert).
- Stochastic Model for Ultraslow diffusion, Stoch. Proc. Appl. Vol. 116, 1215–1235 (2006) (mit M. Meerschaert).
- Aquifer Operator-Scaling and the Effect on Solute Mixing and Dispersion, Water Resources Research, Vol. 42, 1–18 (2006) (mit D.A. Benson, B. Báumer, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand and M. Meerschaert).
- Random walk approximation of fractional-order multiscaling anomalous diffusion, Physical Review E, Vol. 74, 10pp (2006) (mit Yong Zhang, D.A. Benson, E.M. LaBolle, University of California, Davis und M. Meerschaert)
- Operator Scaling Stable Random Fields, Stoch. Proc. Appl. Vol. 117, 312–332 (2007) (mit H. Biermé, Université René Descartes, Paris, France und M. Meerschaert).
- Fourier series approximation of linear fractional stable motion, J. Fourier Analysis Appl. Vol 14, 180 - 202 (2008) (mit Hermine Biermé).
- Triangular array limits for continuous time random walks, Stoch. Proc. Appl. Vol. 118, 1606 - 1633 (2008) (mit Mark Meerschaert).
- Transport of Conservative Solutes in Simulated Fracture Networks 2. Ensemble Solute Transport and the Correspondence to Operator-Stable Limit Distributions, Water Resources Research Vol. 44 (2008) (mit Donald M. Reeves, Desert Research Institute, Reno, Nevada; David A. Benson, Colorado School of Mines, Golden, Colorado and Mark Meerschaert).
- Cluster continuous time random walks, (mit A. Jurlewicz und Mark Meerschaert), Studia Mathematica. Vol 205, 13-30 (2011).
- Multi-operator scaling random fields, (mit Hermine Biermé und Celine Lacaux), Stoch. Proc. Appl. Vol 121, 2642-2677 (2011).
- Application of operator-scaling anisotropic random fields to binary mixtures, (mit D. Anders und A. Hoffmann), Philosophical Magazine Vol 91, (2011).
- Clustered continuous time random walks: Diffusion and relaxation consequences, (mit K. Weron, A. Stanislavsky, A. Jurlewicz und M. Meerschaert), Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Vol 468 1615-1628 (2012)
- Fractional governing equations for coupled random walks, (mit A. Jurlewicz, P. Kern und M.M. Meerschaert), Computers and Mathematics with Applications Vol 64, 3021-3036 (2012).
- Tauberian theorems for matrix regular variation, (mit M. Meerschaert), Transactions of the American Mathematical Society Vol 365, 2207-2221 (2013).
- Simulation of infinitely divisible random fields, (mit Wolgang Karcher und Evgeny Spodarev), Communications in Statistics: Simulation and Computation, 215-246 (2013).
- Parameter estimation for operator scaling random fields, (mit C.Y. Lim und M.M. Meerschaert), Journal of Multivariate Analysis Vol 123,172-183 (2014)
- Extreme value theory with operator norming, (mit M.M. Meerschaert und S. Stoev), Extremes, to appear.
Übersichtsartikel und Arbeiten in Tagungsbänden
- Portfolio Modeling with Heavy Tailed Random Vectors, in Handbook of Heavy Tailed Distributions in Finance, S.T. Rachev (Ed.), Elsevier Science (mit M. Meerschaert) (2003).
- Nonparametric methods for heavy tailed vector data: A survey with applications from finance and hydrology, in Recent Advances and Trends in Nonparametric Statistics, M. G. Akritas and D. N. Politis (Eds.), Elsevier Science (mit M.Meerschaert) (2003).
- Lagrangian characterization of contaminant transport through multidimensional heterogeneous media with limited heterogeneity information, Conference Proceedings for MODFLOW and MORE 2006: Managing Ground-Water Systems, International Ground Water Modeling Center, pp. 639-643 (mit Zhang Yong; David A. Benson; Eric M. LaBolle and M. Meerschaert).
- Efficient simulations of Stable Random Fields and its applications, Stereology and Image Analysis. Ecs10 - Proceedings of the 10th European Congress of ISS, (V.Capasso et al. Eds.) (mit W. Karcher und E. Spodarev) (2009)
Monographien
- Limit Distributions for Sums of Independent Random Vectors, Wiley, New York, 500 Seiten, (mit M. Meerschaert), (2001).
Work in Progress
- Limit Theorems for Implicit Extremes. (mit S. Stoev).
- Limit Theorems for Lévy Walks, (mit P. Straka und M. Magdziarz).
- Tempered Operator Stable Laws, (mit A. Boukali).
- On joint sum/max stability, (mit K. Hees).
- Coupled Continuous Time Random Maxima, (mit K. Hees).
- Operator regularly varying time series (mit J. Goldbach).
- Operator Scaling Random Vector Fields, (mit D. Kremer).