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Author ID: graf.siegfried Recent zbMATH articles by "Graf, Siegfried"
Published as: Graf, Siegfried; Graf, S.
Homepage: http://www.fim.uni-passau.de/ueber-die-fakultaet/ehemalige-professoren/mass-und-...
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Publications by Year

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 0951.60003
Graf, Siegfried; Luschgy, Harald
221
2000
Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Zbl 0823.28003
Bandt, Christoph; Graf, Siegfried
61
1992
Statistically self-similar fractals. Zbl 0591.60005
Graf, Siegfried
49
1987
The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003
Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C.
47
1988
The quantization dimension of self-similar probabilities. Zbl 1010.28009
Graf, Siegfried; Luschgy, Harald
32
2002
On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011
Graf, Siegfried
27
1995
Quantization for probability measures with respect to the geometric mean error. Zbl 1049.60014
Graf, Siegfried; Luschgy, Harald
25
2004
Random homeomorphisms. Zbl 0596.60005
Graf, S.; Mauldin, R. Daniel; Williams, S. C.
24
1986
Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003
Graf, S.; Luschgy, H.
20
2001
Functional quantization and small ball probabilities for Gaussian processes. Zbl 1038.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
19
2003
The quantization of the Cantor distribution. Zbl 0874.28013
Graf, S.; Luschgy, H.
19
1997
The point density measure in the quantization of self-similar probabilities. Zbl 1084.28006
Graf, Siegfried; Luschgy, Harald
18
2005
Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026
Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
17
2004
Distortion mismatch in the quantization of probability measures. Zbl 1196.60062
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
17
2008
The local quantization behavior of absolutely continuous probabilities. Zbl 1260.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
12
2012
A Radon-Nikodym theorem for capacities. Zbl 0434.31004
Graf, Siegfried
10
1980
Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
10
2007
Bisection is not optimal on the average. Zbl 0671.65038
Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros
9
1989
A measurable selection theorem for compact-valued maps. Zbl 0396.28005
Graf, Siegfried
8
1979
A selection theorem for Boolean correspondences. Zbl 0366.06022
Graf, Siegfried
7
1977
Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006
Mauldin, R. D.; Graf, S.; Williams, S. C.
7
1987
On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025
Graf, Siegfried
7
1975
A classification of disintegrations of measures. Zbl 0715.28007
Graf, S.; Mauldin, R. Daniel
7
1989
Quantization for probability measures in the Prokhorov metric. Zbl 1393.60007
Graf, S.; Luschgy, H.
7
2009
Measurable one-to-one selections and transition kernels. Zbl 0573.28013
Graf, Siegfried; Mauldin, R. Daniel
5
1985
On the existence of lower densities in noncomplete measure spaces. Zbl 0344.46098
Graf, Siegfried; von Weizsäcker, Heinrich
5
1976
Induced \(\sigma\)-homomorphisms and a parametrization of measurable sections via extremal preimage measures. Zbl 0411.28023
Graf, Siegfried
5
1980
Rates of convergence for the empirical quantization error. Zbl 1018.60032
Graf, Siegfried; Luschgy, Harald
5
2002
Selected results on measurable selections. Zbl 0509.28007
Graf, Siegfried
3
1982
Homomorphism-compact spaces. Zbl 0525.28013
Babiker, A. G. A. G.; Graf, S.
3
1983
Measurable weak selections. Zbl 0426.28012
Graf, Siegfried
3
1980
Realizing automorphisms of quotients of product \(\sigma\)-fields. Zbl 0426.54025
Graf, Siegfried
3
1982
The average error of quadrature formulas for functions of bounded variation. Zbl 0721.41041
Graf, S.; Novak, E.
3
1990
Isometries of measure algebras. Zbl 0531.28010
Graf, S.; Mägerl, G.
1
1984
Random fractals. Zbl 0849.60003
Graf, Siegfried
1
1991
Sharp asymptotics of the metric entropy for ellipsoids. Zbl 1068.41046
Graf, Siegfried; Luschgy, Harald
1
2004
Entropy-constrained functional quantization of Gaussian processes. Zbl 1079.60032
Graf, Siegfried; Luschgy, Harald
1
2005
Fractal functional quantization of mean-regular stochastic processes. Zbl 1227.60048
Graf, 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 1260.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
12
2012
Fractal functional quantization of mean-regular stochastic processes. Zbl 1227.60048
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
1
2011
Quantization for probability measures in the Prokhorov metric. Zbl 1393.60007
Graf, S.; Luschgy, H.
7
2009
Distortion mismatch in the quantization of probability measures. Zbl 1196.60062
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
17
2008
Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
10
2007
The point density measure in the quantization of self-similar probabilities. Zbl 1084.28006
Graf, Siegfried; Luschgy, Harald
18
2005
Entropy-constrained functional quantization of Gaussian processes. Zbl 1079.60032
Graf, Siegfried; Luschgy, Harald
1
2005
Quantization for probability measures with respect to the geometric mean error. Zbl 1049.60014
Graf, Siegfried; Luschgy, Harald
25
2004
Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026
Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
17
2004
Sharp asymptotics of the metric entropy for ellipsoids. Zbl 1068.41046
Graf, Siegfried; Luschgy, Harald
1
2004
Functional quantization and small ball probabilities for Gaussian processes. Zbl 1038.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
19
2003
The quantization dimension of self-similar probabilities. Zbl 1010.28009
Graf, Siegfried; Luschgy, Harald
32
2002
Rates of convergence for the empirical quantization error. Zbl 1018.60032
Graf, Siegfried; Luschgy, Harald
5
2002
Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003
Graf, S.; Luschgy, H.
20
2001
Foundations of quantization for probability distributions. Zbl 0951.60003
Graf, Siegfried; Luschgy, Harald
221
2000
The quantization of the Cantor distribution. Zbl 0874.28013
Graf, S.; Luschgy, H.
19
1997
On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011
Graf, 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 0823.28003
Bandt, Christoph; Graf, Siegfried
61
1992
Random fractals. Zbl 0849.60003
Graf, Siegfried
1
1991
The average error of quadrature formulas for functions of bounded variation. Zbl 0721.41041
Graf, S.; Novak, E.
3
1990
Bisection is not optimal on the average. Zbl 0671.65038
Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros
9
1989
A classification of disintegrations of measures. Zbl 0715.28007
Graf, S.; Mauldin, R. Daniel
7
1989
The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003
Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C.
47
1988
Statistically self-similar fractals. Zbl 0591.60005
Graf, Siegfried
49
1987
Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006
Mauldin, R. D.; Graf, S.; Williams, S. C.
7
1987
Random homeomorphisms. Zbl 0596.60005
Graf, S.; Mauldin, R. Daniel; Williams, S. C.
24
1986
Measurable one-to-one selections and transition kernels. Zbl 0573.28013
Graf, Siegfried; Mauldin, R. Daniel
5
1985
Isometries of measure algebras. Zbl 0531.28010
Graf, S.; Mägerl, G.
1
1984
Homomorphism-compact spaces. Zbl 0525.28013
Babiker, A. G. A. G.; Graf, S.
3
1983
Selected results on measurable selections. Zbl 0509.28007
Graf, Siegfried
3
1982
Realizing automorphisms of quotients of product \(\sigma\)-fields. Zbl 0426.54025
Graf, Siegfried
3
1982
A Radon-Nikodym theorem for capacities. Zbl 0434.31004
Graf, Siegfried
10
1980
Induced \(\sigma\)-homomorphisms and a parametrization of measurable sections via extremal preimage measures. Zbl 0411.28023
Graf, Siegfried
5
1980
Measurable weak selections. Zbl 0426.28012
Graf, Siegfried
3
1980
A measurable selection theorem for compact-valued maps. Zbl 0396.28005
Graf, Siegfried
8
1979
A selection theorem for Boolean correspondences. Zbl 0366.06022
Graf, Siegfried
7
1977
On the existence of lower densities in noncomplete measure spaces. Zbl 0344.46098
Graf, Siegfried; von Weizsäcker, Heinrich
5
1976
On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025
Graf, Siegfried
7
1975
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

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