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Preprints / Publications

Prof. Dr. Hans-Peter Scheffler

Fachbereich Mathematik

Universität Siegen


Stand: Dezember 2013

Dissertation und Habilitationsschrift

  1. Anziehungsbereiche stabiler Wahrscheinlichkeitsmaße auf stratifizierbaren Lie–Gruppen, Dissertation, Universität Dortmund (1992).
  2. Multivariable R-O variation and generalized domains of semistable attraction, Habilitationsschrift, Universität Dortmund (1997).

Veröffentlichungen in referierten Zeitschriften

  1. 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).
  2. Domains of attraction of stable measures on the Heisenberg group, Probability and Mathematical Statistic, Vol. 14 (1993), pp. 327–345
  3. D–domains of attraction of stable measures on stratified Lie groups, Journal of Theoretical Probability, Vol 7 (1994), pp. 767–792.
  4. Domains of semi–stable attraction of nonnormal semi–stable laws, Journal of Multivariate Analysis, Vol. 51 (1994), pp. 432–444.
  5. Moments of measures attracted to operator semi–stable laws, Statistics and Probability Letters, Vol. 24 (1995), pp. 187–192.
  6. A law of the iterated logarithm for stable laws on stratified Lie groups, Publicationes Mathematicae Debrecen, Vol. 47 (1995), pp. 377–391.
  7. The ”two series theorem” for symmetric random variables on nilpotent Lie groups, Publicationes Mathematicae Debrecen Vol. 47 (1995), pp. 173–179. (mit Daniel Neuenschwander).
  8. 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).
  9. 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).
  10. Series representations for semistable laws and their domains of semistable attraction, Journal of Theoretical Probability Vol. 9 (1996), pp. 931–959, (mit Mark Meerschaert).
  11. Large deviations and law of the iterated logarithm for generalized domains of attraction, Probability and Mathematical Statistics, Vol. 17 (1997), pp. 65–77.
  12. The structure of generalized domains of semistable attraction, Statistics and Probability Letters Vol. 33 (1997), pp. 367–372, (mit Mark Meerschaert).
  13. Spectral decomposition for generalized domains of semistable attraction, Journal of Theoretical Probability Vol. 10 (1997), pp. 51–71, (mit Mark Meerschaert).
  14. 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.
  15. Convergence of semitypes, Publicationes Mathematicae Debrecen Vol. 53 (1998), pp. 119–131, (mit Mark Meerschaert).
  16. 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).
  17. 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).
  18. 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).
  19. Sample covariance matrix for random vectors with heavy tails, J. Theoretical Probab. Vol. 12, pp. 821–838, (1999), (mit Mark Meerschaert).
  20. Moment estimator for random vectors with heavy tails, J. Multivariate Anal. Vol. 71, pp. 145–159 (1999), (mit Mark Meerschaert).
  21. Series representation for operator semistable laws and domains of normal attraction, J. Math. Science Vol. 92 (4) (1999) pp. 4062–4084.
  22. On estimation of the spectral measure of certain nonnormal operator stable laws, Statistics and Probability Letters Vol. 43, 385–392 (1999).
  23. Multivariable Regular Variation of Functions and Measures, Journal Applied Analysis Vol. 5, pp. 125–146 (1999), (mit Mark Meerschaert).
  24. One-dimensional marginals of operator stable laws and their domains of attraction, Publ. Math. Debrecen Vol. 55, pp. 487–499 (1999), (mit Mark Meerschaert).
  25. 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).
  26. Strongly τ-decomposable and selfdecomposable laws on simply connected nilpotent Lie groups, Monatshefte Math. Vol. 128, pp. 269–282 (1999), (mit W. Hazod).
  27. Moving averages of random vectors with regularly varying tails, J. Time Series Anal. Vol. 21 (3), pp. 297–328 (2000) (mit Mark Meerschaert).
  28. Limit laws for symmetric k-tensors of regularly varying measures, J. Multivariate Anal. Vol. 73, pp. 241–261 (2000), (mit Mark Meerschaert).
  29. Multivariate R-O varying measures. Part I: Uniform bounds, Proc. London Math. Soc. Vol. 81 (3) (2000), pp. 231–256.
  30. A law of the iterated logarithm for heavy tailed random vectors, Prob. Theory Related Fields Vol. 116 (2000), pp. 257–271.
  31. 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).
  32. Norming operators for generalized domains of semistable attraction, Publ. Math. Debrecen Vol. 58, pp. 391–409 (2001).
  33. Sample cross-correlations for moving averages with regularly varying tails, J. Time Series Anal. Vol. 22 (4), pp. 481–492 (2001), (mit Mark Meerschaert).
  34. Multivariate R-O varying measures. Part II: Individual bounds, J. Math. Science. Vol. 111 (6) (2002), pp. 3868–3878.
  35. Semistable Lévy Motion, Fractional Calculus and Applied Analysis Vol. 5 (2002), pp. 27–54 (mit M. Meerschaert).
  36. 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).
  37. 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).
  38. Hausdorff Dimension of operator stable sample path, Monatshefte Mathematik Vol. 140, 91–101 (2003), (mit M. Meerschaert und P. Becker-Kern).
  39. Precise Asymptotics in Spitzer’s and Baum-Katz Law of Large Numbers: The semistable case, J. Math. Anal. Appl. Vol. 288, 285–298, (2003).
  40. 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).
  41. Limit Theorems for Coupled Continuous Time Random Walks, Annals Probab. Vol. 32, 730–756 (mit P. Becker-Kern und M.Meerschaert) (2004).
  42. 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).
  43. Limit theorems for continuous time random walks with infinite mean waiting times, J Appl. Probab. Vol. 41, 623–638 (2004), (mit M. Meerschaert).
  44. On multiple particle continuous time random walks, J. Appl. Math. Vol. 2004:3, 213–233 (2004), (mit P. Becker-Kern).
  45. Limiting Behavior of Weighted Sums of Heavy-tailed Random Vectors and Applications, Probab. Math. Stat. Vol. 24, 281–295, (2004) (mit Chen Pingyan)
  46. 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).
  47. 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).
  48. Limit theorems for continuous time random walks with slowly varying waiting times, Stoch. Probab. Letters Vol. 71, 15–22 (2005), (mit M. Meerschaert).
  49. 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).
  50. How to find stability in a purely semistable context, Yokohama Mathematical Journal, Vol. 51, 75–88, (2005), (mit P. Becker-Kern).
  51. 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).
  52. 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).
  53. 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).
  54. Stochastic Model for Ultraslow diffusion, Stoch. Proc. Appl. Vol. 116, 1215–1235 (2006) (mit M. Meerschaert).
  55. 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).
  56. 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)
  57. Operator Scaling Stable Random Fields, Stoch. Proc. Appl. Vol. 117, 312–332 (2007) (mit H. Biermé, Université René Descartes, Paris, France und M. Meerschaert).
  58. Fourier series approximation of linear fractional stable motion, J. Fourier Analysis Appl. Vol 14, 180 - 202 (2008) (mit Hermine Biermé).  
  59. Triangular array limits for continuous time random walks, Stoch. Proc. Appl. Vol. 118, 1606 - 1633 (2008) (mit Mark Meerschaert).
  60. 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).
  61. Cluster continuous time random walks, (mit A. Jurlewicz und Mark Meerschaert), Studia Mathematica. Vol 205, 13-30 (2011).
  62.  Multi-operator scaling random fields, (mit Hermine Biermé und Celine Lacaux), Stoch. Proc. Appl. Vol 121, 2642-2677 (2011).
  63. Application of operator-scaling anisotropic random fields to binary mixtures, (mit D. Anders und A. Hoffmann),  Philosophical Magazine Vol 91, (2011).
  64. 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)
  65. 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).
  66. Tauberian theorems for matrix regular variation,  (mit M. Meerschaert), Transactions of the American Mathematical Society Vol 365, 2207-2221 (2013).
  67. Simulation of infinitely divisible random fields, (mit Wolgang Karcher und Evgeny Spodarev), Communications in Statistics: Simulation and Computation, 215-246 (2013).
  68. Parameter estimation for operator scaling random fields, (mit C.Y. Lim und M.M. Meerschaert), Journal of Multivariate Analysis Vol 123,172-183 (2014)
  69. Extreme value theory with operator norming, (mit M.M. Meerschaert und S. Stoev), Extremes, to appear.

Übersichtsartikel und Arbeiten in Tagungsbänden

  1. 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).
  2. 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).
  3. 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).
  4. 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)


  1. Limit Distributions for Sums of Independent Random Vectors, Wiley, New York, 500 Seiten, (mit M. Meerschaert), (2001).

Work in Progress

  1. Limit Theorems for Implicit Extremes. (mit S. Stoev).
  2. Limit Theorems for Lévy Walks, (mit P. Straka und M. Magdziarz).
  3. Tempered Operator Stable Laws, (mit A. Boukali).
  4. On joint sum/max stability, (mit K. Hees).
  5. Coupled Continuous Time Random Maxima, (mit K. Hees).
  6. Operator regularly varying time series (mit J. Goldbach).
  7. Operator Scaling Random Vector Fields, (mit D. Kremer).
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