Edit Profile (opens in new tab) Graf, Siegfried Compute Distance To: Compute Author ID: graf.siegfried Published as: Graf, Siegfried; Graf, S. Homepage: http://www.fim.uni-passau.de/ueber-die-fakultaet/ehemalige-professoren/mass-und-... External Links: MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 51 Publications since 1974, including 2 Books 3 Contributions as Editor · 1 Further Contribution Co-Authors: 13 Co-Authors with 36 Joint Publications 290 Co-Co-Authors all top 5 Co-Authors 19 single-authored 17 Luschgy, Harald 7 Pagès, Gilles 6 Mauldin, Richard Daniel 3 Bandt, Christoph 3 Mägerl, Gerhard 3 Novak, Erich 2 Delattre, Sylvain 2 Maharam Stone, Dorothy 2 Papageorgiou, Anargyros 2 Zähle, Martina 1 Babiker, A. G. A. G. 1 Christensen, Jens Peter Reus 1 Erdős, Pál 1 Kölzow, Dietrich 1 Shortt, Rae Michael 1 von Weizsäcker, Heinrich all top 5 Serials 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Proceedings of the American Mathematical Society 2 The Annals of Probability 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Nachrichten 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Real Analysis Exchange 2 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 2 Journal of Complexity 2 Progress in Probability 2 Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 Theory of Probability and its Applications 1 Advances in Mathematics 1 American Journal of Mathematics 1 Canadian Journal of Mathematics 1 Journal of Approximation Theory 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Topology and its Applications 1 Statistics & Decisions 1 Probability Theory and Related Fields 1 Journal of Theoretical Probability 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Proceedings of the National Academy of Sciences of the United States of America 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Lecture Notes in Mathematics all top 5 Fields 33 Measure and integration (28-XX) 27 Probability theory and stochastic processes (60-XX) 10 General topology (54-XX) 6 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 3 Approximations and expansions (41-XX) 3 Statistics (62-XX) 2 Mathematical logic and foundations (03-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 39 Publications have been cited 721 times in 486 Documents Cited by ▼ Year ▼ Foundations of quantization for probability distributions. Zbl 0951.60003Graf, Siegfried; Luschgy, Harald 221 2000 Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Zbl 0823.28003Bandt, Christoph; Graf, Siegfried 61 1992 Statistically self-similar fractals. Zbl 0591.60005Graf, Siegfried 49 1987 The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C. 47 1988 The quantization dimension of self-similar probabilities. Zbl 1010.28009Graf, Siegfried; Luschgy, Harald 32 2002 On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011Graf, Siegfried 27 1995 Quantization for probability measures with respect to the geometric mean error. Zbl 1049.60014Graf, Siegfried; Luschgy, Harald 25 2004 Random homeomorphisms. Zbl 0596.60005Graf, S.; Mauldin, R. Daniel; Williams, S. C. 24 1986 Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003Graf, S.; Luschgy, H. 20 2001 Functional quantization and small ball probabilities for Gaussian processes. Zbl 1038.60032Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 19 2003 The quantization of the Cantor distribution. Zbl 0874.28013Graf, S.; Luschgy, H. 19 1997 The point density measure in the quantization of self-similar probabilities. Zbl 1084.28006Graf, Siegfried; Luschgy, Harald 18 2005 Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 17 2004 Distortion mismatch in the quantization of probability measures. Zbl 1196.60062Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 17 2008 The local quantization behavior of absolutely continuous probabilities. Zbl 1260.60032Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 12 2012 A Radon-Nikodym theorem for capacities. Zbl 0434.31004Graf, Siegfried 10 1980 Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 10 2007 Bisection is not optimal on the average. Zbl 0671.65038Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros 9 1989 A measurable selection theorem for compact-valued maps. Zbl 0396.28005Graf, Siegfried 8 1979 A selection theorem for Boolean correspondences. Zbl 0366.06022Graf, Siegfried 7 1977 Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006Mauldin, R. D.; Graf, S.; Williams, S. C. 7 1987 On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025Graf, Siegfried 7 1975 A classification of disintegrations of measures. Zbl 0715.28007Graf, S.; Mauldin, R. Daniel 7 1989 Quantization for probability measures in the Prokhorov metric. Zbl 1393.60007Graf, S.; Luschgy, H. 7 2009 Measurable one-to-one selections and transition kernels. Zbl 0573.28013Graf, Siegfried; Mauldin, R. Daniel 5 1985 On the existence of lower densities in noncomplete measure spaces. Zbl 0344.46098Graf, Siegfried; von Weizsäcker, Heinrich 5 1976 Induced \(\sigma\)-homomorphisms and a parametrization of measurable sections via extremal preimage measures. Zbl 0411.28023Graf, Siegfried 5 1980 Rates of convergence for the empirical quantization error. Zbl 1018.60032Graf, Siegfried; Luschgy, Harald 5 2002 Selected results on measurable selections. Zbl 0509.28007Graf, Siegfried 3 1982 Homomorphism-compact spaces. Zbl 0525.28013Babiker, A. G. A. G.; Graf, S. 3 1983 Measurable weak selections. Zbl 0426.28012Graf, Siegfried 3 1980 Realizing automorphisms of quotients of product \(\sigma\)-fields. Zbl 0426.54025Graf, Siegfried 3 1982 The average error of quadrature formulas for functions of bounded variation. Zbl 0721.41041Graf, S.; Novak, E. 3 1990 Isometries of measure algebras. Zbl 0531.28010Graf, S.; Mägerl, G. 1 1984 Random fractals. Zbl 0849.60003Graf, Siegfried 1 1991 Sharp asymptotics of the metric entropy for ellipsoids. Zbl 1068.41046Graf, Siegfried; Luschgy, Harald 1 2004 Entropy-constrained functional quantization of Gaussian processes. Zbl 1079.60032Graf, Siegfried; Luschgy, Harald 1 2005 Fractal functional quantization of mean-regular stochastic processes. Zbl 1227.60048Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 1 2011 Fractal geometry and stochastics. Proceedings of a conference on fractal geometry and stochastics held at Finsterbergen, Germany, June 12-18, 1994. Zbl 0829.00021 1 1995 The local quantization behavior of absolutely continuous probabilities. Zbl 1260.60032Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 12 2012 Fractal functional quantization of mean-regular stochastic processes. Zbl 1227.60048Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 1 2011 Quantization for probability measures in the Prokhorov metric. Zbl 1393.60007Graf, S.; Luschgy, H. 7 2009 Distortion mismatch in the quantization of probability measures. Zbl 1196.60062Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 17 2008 Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 10 2007 The point density measure in the quantization of self-similar probabilities. Zbl 1084.28006Graf, Siegfried; Luschgy, Harald 18 2005 Entropy-constrained functional quantization of Gaussian processes. Zbl 1079.60032Graf, Siegfried; Luschgy, Harald 1 2005 Quantization for probability measures with respect to the geometric mean error. Zbl 1049.60014Graf, Siegfried; Luschgy, Harald 25 2004 Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 17 2004 Sharp asymptotics of the metric entropy for ellipsoids. Zbl 1068.41046Graf, Siegfried; Luschgy, Harald 1 2004 Functional quantization and small ball probabilities for Gaussian processes. Zbl 1038.60032Graf, Siegfried; Luschgy, Harald; Pagès, Gilles 19 2003 The quantization dimension of self-similar probabilities. Zbl 1010.28009Graf, Siegfried; Luschgy, Harald 32 2002 Rates of convergence for the empirical quantization error. Zbl 1018.60032Graf, Siegfried; Luschgy, Harald 5 2002 Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003Graf, S.; Luschgy, H. 20 2001 Foundations of quantization for probability distributions. Zbl 0951.60003Graf, Siegfried; Luschgy, Harald 221 2000 The quantization of the Cantor distribution. Zbl 0874.28013Graf, S.; Luschgy, H. 19 1997 On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011Graf, Siegfried 27 1995 Fractal geometry and stochastics. Proceedings of a conference on fractal geometry and stochastics held at Finsterbergen, Germany, June 12-18, 1994. Zbl 0829.00021 1 1995 Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Zbl 0823.28003Bandt, Christoph; Graf, Siegfried 61 1992 Random fractals. Zbl 0849.60003Graf, Siegfried 1 1991 The average error of quadrature formulas for functions of bounded variation. Zbl 0721.41041Graf, S.; Novak, E. 3 1990 Bisection is not optimal on the average. Zbl 0671.65038Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros 9 1989 A classification of disintegrations of measures. Zbl 0715.28007Graf, S.; Mauldin, R. Daniel 7 1989 The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C. 47 1988 Statistically self-similar fractals. Zbl 0591.60005Graf, Siegfried 49 1987 Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006Mauldin, R. D.; Graf, S.; Williams, S. C. 7 1987 Random homeomorphisms. Zbl 0596.60005Graf, S.; Mauldin, R. Daniel; Williams, S. C. 24 1986 Measurable one-to-one selections and transition kernels. Zbl 0573.28013Graf, Siegfried; Mauldin, R. Daniel 5 1985 Isometries of measure algebras. Zbl 0531.28010Graf, S.; Mägerl, G. 1 1984 Homomorphism-compact spaces. Zbl 0525.28013Babiker, A. G. A. G.; Graf, S. 3 1983 Selected results on measurable selections. Zbl 0509.28007Graf, Siegfried 3 1982 Realizing automorphisms of quotients of product \(\sigma\)-fields. Zbl 0426.54025Graf, Siegfried 3 1982 A Radon-Nikodym theorem for capacities. Zbl 0434.31004Graf, Siegfried 10 1980 Induced \(\sigma\)-homomorphisms and a parametrization of measurable sections via extremal preimage measures. Zbl 0411.28023Graf, Siegfried 5 1980 Measurable weak selections. Zbl 0426.28012Graf, Siegfried 3 1980 A measurable selection theorem for compact-valued maps. Zbl 0396.28005Graf, Siegfried 8 1979 A selection theorem for Boolean correspondences. Zbl 0366.06022Graf, Siegfried 7 1977 On the existence of lower densities in noncomplete measure spaces. Zbl 0344.46098Graf, Siegfried; von Weizsäcker, Heinrich 5 1976 On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025Graf, Siegfried 7 1975 all cited Publications top 5 cited Publications all top 5 Cited by 558 Authors 38 Pagès, Gilles 26 Zhu, Sanguo 21 Roychowdhury, Mrinal Kanti 16 Luschgy, Harald 11 Graf, Siegfried 8 Bandt, Christoph 8 Hu, Dihe 8 Macheras, Nikolaos Demetrios 8 Mauldin, Richard Daniel 8 Pichler, Alois 7 Kreitmeier, Wolfgang 6 Matsuura, Shun 6 Novak, Erich 6 Sagna, Abass 6 Strauss, Werner 5 Dereich, Steffen 5 Falconer, Kenneth J. 5 Fiorin, Lucio 5 Musial, Kazimierz 5 Patzschke, Norbert 5 Ritter, Klaus 5 Troscheit, Sascha 4 Barral, Julien 4 Callegaro, Giorgia 4 Fort, Jean-Claude 4 Fraser, Jonathan MacDonald 4 Hambly, Ben M. 4 Iacobelli, Mikaela 4 Kesseböhmer, Marc 4 Kurata, Hiroshi 4 Molchanov, Ilya S. 4 Monticino, Michael G. 4 Mörters, Peter 4 Peres, Yuval 4 Pflug, Georg Ch. 4 Pham, Huyên 4 Printems, Jacques 4 Römisch, Werner 4 Simon, Károly 4 Solomyak, Boris 4 Staiger, Ludwig 4 Tarpey, Thaddeus 4 Tetenov, Andreĭ Viktorovich 4 Zähle, Martina 3 Barnsley, Michael Fielding 3 Berger, Arno 3 Çömez, Doḡan 3 Dai, Meifeng 3 Elekes, Márton 3 Feng, De-Jun 3 Grekas, Stratos 3 Heitsch, Holger 3 Hutchinson, John Edward 3 Jourdain, Benjamin 3 Kamalutdinov, Kirill Glebovich 3 Le Gouic, Thibaut 3 Patacchini, Francesco Saverio 3 Rams, Michał 3 Sugeno, Michio 3 Torra, Vicenç 3 Wilbertz, Benedikt 3 Xi, Lifeng 3 Xu, Chuang 3 Zhou, Youming 2 Aswathy, R. K. 2 Aurzada, Frank 2 Bally, Vlad 2 Bárány, Balázs 2 Bardou, Olivier 2 Ben Mabrouk, Anouar 2 Berlinkov, Artemi 2 Bluhm, Christian E. 2 Bogachev, Vladimir Igorevich 2 Boissard, Emmanuel 2 Bonnans, Joseph Frédéric 2 Borisovich, Yuriĭ Grigor’evich 2 Borodachov, Sergiy V. 2 Bourne, David P. 2 Bouthemy, Sandrine 2 Bronstein, Anne Laure 2 Burke, Maxim R. 2 Caglioti, Emanuele 2 Caliebe, Amke 2 Charlier, Isabelle 2 Corlay, Sylvain 2 Creutzig, Jakob 2 Croydon, David A. 2 del Barrio, Eustasio 2 Delarue, François 2 Delattre, Sylvain 2 Fang, Kai-Tai 2 Gelbrich, Götz 2 Gel’man, Boris Danielovich 2 Golse, François 2 Grasselli, Martino 2 Gruber, Peter Manfred 2 He, Ping 2 Järvenpää, Esa 2 Käärik, Meelis 2 Kiss, Viktor ...and 458 more Authors all top 5 Cited in 188 Serials 27 Journal of Mathematical Analysis and Applications 23 Proceedings of the American Mathematical Society 14 Chaos, Solitons and Fractals 14 Stochastic Processes and their Applications 12 Advances in Mathematics 11 Israel Journal of Mathematics 11 Probability Theory and Related Fields 9 The Annals of Probability 9 Transactions of the American Mathematical Society 9 Bernoulli 7 Journal of Approximation Theory 7 Monatshefte für Mathematik 7 The Annals of Applied Probability 7 Quantitative Finance 6 Journal of Statistical Planning and Inference 6 Mathematische Zeitschrift 6 Ergodic Theory and Dynamical Systems 6 Journal of Theoretical Probability 6 Wuhan University Journal of Natural Sciences (WUJNS) 5 Communications in Mathematical Physics 5 Topology and its Applications 5 Journal of Complexity 5 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 5 Fractals 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 The Annals of Statistics 4 Mathematische Nachrichten 4 Advances in Applied Mathematics 4 Statistics & Probability Letters 4 Mathematical Programming. Series A. Series B 4 Monte Carlo Methods and Applications 4 Discrete and Continuous Dynamical Systems 4 Foundations of Computational Mathematics 3 Advances in Applied Probability 3 The Mathematical Intelligencer 3 Fuzzy Sets and Systems 3 Journal of Functional Analysis 3 Mathematika 3 Memoirs of the American Mathematical Society 3 Forum Mathematicum 3 Annals of Operations Research 3 Calculus of Variations and Partial Differential Equations 3 Statistical Papers 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Methodology and Computing in Applied Probability 3 Stochastics and Dynamics 3 Analysis in Theory and Applications 3 Electronic Journal of Statistics 3 Science China. Mathematics 2 Automatica 2 Geometriae Dedicata 2 Journal of the American Statistical Association 2 Journal of Computational and Applied Mathematics 2 Journal of Multivariate Analysis 2 Journal of Soviet Mathematics 2 Mathematische Annalen 2 Mathematics of Operations Research 2 Numerische Mathematik 2 Real Analysis Exchange 2 Zeitschrift für Analysis und ihre Anwendungen 2 Acta Mathematica Hungarica 2 Acta Applicandae Mathematicae 2 Order 2 Constructive Approximation 2 Statistical Science 2 Aequationes Mathematicae 2 Communications in Statistics. Theory and Methods 2 European Journal of Operational Research 2 Journal of Statistical Computation and Simulation 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Stochastics and Stochastics Reports 2 Computational Optimization and Applications 2 Applied Mathematical Finance 2 The Journal of Fourier Analysis and Applications 2 Mathematical Finance 2 Acta Mathematica Sinica. English Series 2 Dynamical Systems 2 Kyoto Journal of Mathematics 1 Modern Physics Letters A 1 Archive for Rational Mechanics and Analysis 1 Biological Cybernetics 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Information Processing Letters 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Mathematical Notes 1 Nonlinearity 1 Problems of Information Transmission 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Ukrainian Mathematical Journal 1 Arkiv för Matematik 1 Mathematics of Computation 1 Algebra Universalis 1 Annali di Matematica Pura ed Applicata. Serie Quarta ...and 88 more Serials all top 5 Cited in 44 Fields 223 Measure and integration (28-XX) 210 Probability theory and stochastic processes (60-XX) 75 Statistics (62-XX) 56 Dynamical systems and ergodic theory (37-XX) 50 Numerical analysis (65-XX) 45 Information and communication theory, circuits (94-XX) 30 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 28 Operations research, mathematical programming (90-XX) 20 General topology (54-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 17 Approximations and expansions (41-XX) 14 Computer science (68-XX) 12 Functional analysis (46-XX) 11 Partial differential equations (35-XX) 11 Convex and discrete geometry (52-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Mathematical logic and foundations (03-XX) 8 Real functions (26-XX) 8 Systems theory; control (93-XX) 6 Combinatorics (05-XX) 6 Abstract harmonic analysis (43-XX) 6 Operator theory (47-XX) 5 Number theory (11-XX) 5 Topological groups, Lie groups (22-XX) 5 Differential geometry (53-XX) 4 Category theory; homological algebra (18-XX) 4 Group theory and generalizations (20-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Difference and functional equations (39-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 General algebraic systems (08-XX) 2 Potential theory (31-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.