Faculty of Computer Science and Mathematics
Publications

Publications

Books

  • Foundations of quantization for probability distributions. Lect. Notes in Math. 1730, Springer 2000 (jointly with H. Luschgy)

Contributions to Journals

  • Fractal functional quantization of mean-regular stochastic processes. Math. Proc. Camb. Phil. Soc. 150, 167-191 (2011) (jointly with H. Luschgy and G. Pagès)
  • Quantization for probability measures in the Prokhorov Metric. Theory Probab. Appl., Volume 53, No. 2, 216-241 (2009) (jointly with H. Luschgy)

  • Distortion mismatch in the quantization of probability measures. ESAIM: Probability and Statistics 12, 127-153 (2008) (jointly with H. Luschgy, G. Pagès)
  • Optimal quantizers for Radon random vectors in a Banach space. J. Approximation Theory 144, 27-53 (2007) (jointly with H. Luschgy, G. Pagès)

  • Quantization of probability distributions under norm-based distortion measures II: self-similar distributions. J. Math. Analysis Appl. 318, 507- 516 (2006) (jointly with S. Dellattre, H. Luschgy, G. Pagès)
  • Entropy-constrained functional quantization of Gaussian processes. Proc. Amer. Math. Soc. 133, 3403-3409 (2005) (jointly with H. Luschgy)
  • The point density measure in the quantization of self-similar probabilities. Math. Proc. Cambridge Phil. Soc 138, 513-531 (2005) (jointly with H. Luschgy)

  • Quantization of probability distributions under norm-based distortion measures. Statistics and Decisions 22, 261-282 (2004) (jointly with S. Dellattre, H. Luschgy, G. Pagès)

  • Sharp asymptotics of the metric entropy for ellipsoids. J. Complexity 20, 876-882 (2004) (jointly with H. Luschgy)

  • Quantization for probability measures with respect to the geometric mean error.  Math. Proc. Camb. Phil. Soc. 136, 687-717 (2004) (jointly with H. Luschgy)

  • Functional quantization and small ball probabilities for Gaussian processes. J. Theor. Prob. 16, 1047-1062 (2003) (jointly with H. Luschgy und G. Pagès)

  • The quantization dimension of self-similar probabilities. Math. Nachrichten 241, 103-109 (2002) (jointly with H. Luschgy)

  • Rates of convergence for the empirical quantization error. Annals of Probability 30, 874-897 (2002) (jointly with H. Luschgy)

  • Asymptotics of the quantization errors for self-similar probabilities. Real Analysis Exchange 26, 795-810 (2000/01) (jointly with H. Luschgy)

  • The quantization of the Cantor distribution. Math. Nachr. 183, 113-133 (1997) (jointly with H. Luschgy)

  • On Bandt's tangential distribution for self-similar measures. Monatshefte für Mathematik 120, 223-246 (1995)

  • On the characterization of the Hausdorff measure on a self-similar set. Atti. Sem. Mat. Fis. Modena 42, 189-197 (1994)

  • Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Proc. Amer. math. Soc. 114, 995-1001 (1992) (jointly with C. Bandt)

  • The average error of quadrature formulas for functions of bounded variation. Rocky Mountain J. Math. 20, 707-716 (1990) (jointly with E. Novak)

  • A classification of disintegrations of measures. Contemporary Math. 94, 147-158 (1989) (jointly with R.D. Mauldin)

  • Bisection is not optimal on the average. Numer. Maths. 55, 481-491 (1989) (jointly with E. Novak)

  • The exact Hausdorff dimension in random recursive constructions. Mem. Amer. math. Soc. 71, No. 381 (1988) (jointly with R.D. Mauldin und S.C. Williams)

  • Statistically self-similar fractals. Probability Theory and Rel. Fields 74, 357-392 (1987)

  • Random homeomorphisms. Advances Math. 60, 239-359 (1986) (jointly with R.D. Mauldin und S.C. Williams)

  • Measurable one-to-one selections and transition kernels. Amer. J. Math. 106, 407-425 (1984) (jointly withR.D. Mauldin)

  • Isometries of measure algebras. Monatshefte für Mathematik 97, 107-118 (1984) (jointly with G. Mägerl)

  • Homomorphism compact spaces. Canadian J. Math. 35, 558-576 (1983) (jointly with  A.G.A.G. Babiker)

  • Baire sections for group homeomorphisms. Proc. Amer. Math. Soc. 85, 615-618 (1982) (jointly with G. Mägerl)

  • Realizing automorphisms of quotients of product sigma-fields. Pacific J. Math. 99, 19-30 (1982)

  • A note on realizing homomorphisms of category algebras. General Topology and Its Appl. 12, 247-256 (1981)

  • A Radon-Nikodym theorem for capacites. J. reine u. angew. Math. 320, 192-214 (1980)

  • Induced sigma-homeomorphisms and a parametrization of measurable sections via extremal preimage measures. Math. Ann. 247, 67-80 (1980)

  • A measurable selection theorem for compact-valued maps. Manuscripta Math. 27, 341-352 (1979)

  • A selection theorem for Boolean correspondences. J. reine u. angew. Math. 295, 169-186 (1977)

  • On the existence of strong liftings in second countable topological spaces. Pacific J. Math. 58, 419-426 (1975)

Conference Proceedings

  • The quantization of probability distributions: Some results and open problems. Real Analysis Exchange Summer Symposium 2002, 87-102
  • Consistent estimation in the quantization problem for random vectors. In: Transaction of the 12th Prague Conference on Information Theory. Statistical Decision Functions, Random Processes, Acad. Sci. Czech Republic & Charles Univ. Prague, Prague 1994, pp. 84-87 (mit H. Luschgy)
  • Self-similar sets and measures. Rendiconti dell'istituto di matematica dell'universita di Trieste 26, 36-47 (1994)
  • Barnsley's scheme for the fractal encoding of images. J. Complexity 8, 72-78 (1992)
  • Note on question 4 of D. Maharam. In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in Math. 1089, Springer, Berlin-Heidelberg-New York 1984, p. 319
  • Random homeomorphisms (Kurzfassung). In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in Math. 1089, Springer, Berlin-Heidelberg-New York 1984, pp. 23-46 (mit R.D. Mauldin und S.C. Williams)
  • Selected results on measureable selections. In: Proc. of the Tenth Winter School on Abstract Analysis, Suppl. Rend. Circ. Mat. Palermo, Ser. II(2), 87-122 (1982)
  • Disintegration of a measure with respect to a correspondence. In: Measure Theory, Oberwolfach 1983 (D. Kölzow, D. Maharam.Stone eds.), Lect. Notes in math. 945, Springer, Berlin-Heidelberg-New York 1982, pp. 167-169 (with G. Mägerl)
  • Families of pairwise orthogonal measures. In: Proc. of the Ninth Winter School on Abstract Analysis, Czech. Acad. Sci., Prague 1981 (with G. Mägerl)
  • Measurable weak selections. In: Measure Theory, Oberwolfach 1979 (D. Kölzow ed.), Lect. Notes in Math. 794, Springer, Berlin-Heidelberg-New York 1980, pp. 117-140
  • On the existence of lower densities in noncomplete measure spaces. In: Measure Theory, Oberwolfach 1975 (D. Kölzow, A. Bellow eds.), Lect. Notes in Math. 541, Springer, Berlin-Heidelberg-New York 1976, pp. 155-158 (mit H. von Weizsäcker)

Reports

  • The quantization dimension of self-similar sets, MIP-9609, Universität Passau 1996
  • Foundations of quantization for random vectors. Preprint Nr. 16, Angewandte Mathematik und Informatik, Universität Münster 1994 (mit H. Luschgy)
  • The equidistribution on self-similar fractals. MIP-8929, Universität Passau 1989