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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

41 Publications have been cited 846 times in 578 Documents Cited by Year
Foundations of quantization for probability distributions. Zbl 0951.60003
Graf, Siegfried; Luschgy, Harald
277
2000
Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Zbl 0823.28003
Bandt, Christoph; Graf, Siegfried
70
1992
Statistically self-similar fractals. Zbl 0591.60005
Graf, Siegfried
55
1987
The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003
Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C.
53
1988
The quantization dimension of self-similar probabilities. Zbl 1010.28009
Graf, Siegfried; Luschgy, Harald
34
2002
On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011
Graf, Siegfried
31
1995
Quantization for probability measures with respect to the geometric mean error. Zbl 1049.60014
Graf, Siegfried; Luschgy, Harald
29
2004
Random homeomorphisms. Zbl 0596.60005
Graf, S.; Mauldin, R. Daniel; Williams, S. C.
26
1986
Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003
Graf, S.; Luschgy, H.
24
2001
The quantization of the Cantor distribution. Zbl 0874.28013
Graf, S.; Luschgy, H.
23
1997
Distortion mismatch in the quantization of probability measures. Zbl 1196.60062
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
21
2008
Functional quantization and small ball probabilities for Gaussian processes. Zbl 1038.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
21
2003
Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026
Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
18
2004
The point density measure in the quantization of self-similar probabilities. Zbl 1084.28006
Graf, Siegfried; Luschgy, Harald
18
2005
The local quantization behavior of absolutely continuous probabilities. Zbl 1260.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
16
2012
A classification of disintegrations of measures. Zbl 0715.28007
Graf, S.; Mauldin, R. Daniel
13
1989
A Radon-Nikodym theorem for capacities. Zbl 0434.31004
Graf, Siegfried
11
1980
Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
11
2007
Bisection is not optimal on the average. Zbl 0671.65038
Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros
9
1989
Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006
Mauldin, R. D.; Graf, S.; Williams, S. C.
8
1987
A measurable selection theorem for compact-valued maps. Zbl 0396.28005
Graf, Siegfried
8
1979
On the existence of lower densities in noncomplete measure spaces. Zbl 0344.46098
Graf, Siegfried; von Weizsäcker, Heinrich
8
1976
Quantization for probability measures in the Prokhorov metric. Zbl 1393.60007
Graf, S.; Luschgy, H.
7
2009
On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025
Graf, Siegfried
7
1975
A selection theorem for Boolean correspondences. Zbl 0366.06022
Graf, Siegfried
7
1977
Rates of convergence for the empirical quantization error. Zbl 1018.60032
Graf, Siegfried; Luschgy, Harald
6
2002
Measurable one-to-one selections and transition kernels. Zbl 0573.28013
Graf, Siegfried; Mauldin, R. Daniel
5
1985
Induced \(\sigma\)-homomorphisms and a parametrization of measurable sections via extremal preimage measures. Zbl 0411.28023
Graf, Siegfried
5
1980
Selected results on measurable selections. Zbl 0509.28007
Graf, Siegfried
4
1982
Measurable weak selections. Zbl 0426.28012
Graf, Siegfried
4
1980
The average error of quadrature formulas for functions of bounded variation. Zbl 0721.41041
Graf, S.; Novak, E.
3
1990
Homomorphism-compact spaces. Zbl 0525.28013
Babiker, A. G. A. G.; Graf, S.
3
1983
Realizing automorphisms of quotients of product \(\sigma\)-fields. Zbl 0426.54025
Graf, Siegfried
3
1982
Fractal geometry and stochastics. Proceedings of a conference on fractal geometry and stochastics held at Finsterbergen, Germany, June 12-18, 1994. Zbl 0829.00021
2
1995
Isometries of measure algebras. Zbl 0531.28010
Graf, S.; Mägerl, G.
1
1984
Fractal functional quantization of mean-regular stochastic processes. Zbl 1227.60048
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
1
2011
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
Random fractals. Zbl 0849.60003
Graf, Siegfried
1
1991
Problem section of Conf. on Measure Theory. Zbl 0549.28002
1
1984
The quantization of probability distributions: some results and open problems. Zbl 1103.94013
Graf, Siegfried
1
2002
The local quantization behavior of absolutely continuous probabilities. Zbl 1260.60032
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
16
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
21
2008
Optimal quantizers for Radon random vectors in a Banach space. Zbl 1107.60003
Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
11
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
29
2004
Quantization of probability distributions under norm-based distortion measures. Zbl 1066.60026
Delattre, Sylvain; Graf, Siegfried; Luschgy, Harald; Pagès, Gilles
18
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
21
2003
The quantization dimension of self-similar probabilities. Zbl 1010.28009
Graf, Siegfried; Luschgy, Harald
34
2002
Rates of convergence for the empirical quantization error. Zbl 1018.60032
Graf, Siegfried; Luschgy, Harald
6
2002
The quantization of probability distributions: some results and open problems. Zbl 1103.94013
Graf, Siegfried
1
2002
Asymptotics of the quantization errors for self-similar probabilities. Zbl 1029.28003
Graf, S.; Luschgy, H.
24
2001
Foundations of quantization for probability distributions. Zbl 0951.60003
Graf, Siegfried; Luschgy, Harald
277
2000
The quantization of the Cantor distribution. Zbl 0874.28013
Graf, S.; Luschgy, H.
23
1997
On Bandt’s tangential distribution for self-similar measures. Zbl 0841.28011
Graf, Siegfried
31
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
2
1995
Self-similar sets 7. A characterization of self-similar fractals with positive Hausdorff measure. Zbl 0823.28003
Bandt, Christoph; Graf, Siegfried
70
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
A classification of disintegrations of measures. Zbl 0715.28007
Graf, S.; Mauldin, R. Daniel
13
1989
Bisection is not optimal on the average. Zbl 0671.65038
Graf, Siegfried; Novak, Erich; Papageorgiou, Anargyros
9
1989
The exact Hausdorff dimension in random recursive constructions. Zbl 0641.60003
Graf, Siegfried; Mauldin, R. Daniel; Williams, S. C.
53
1988
Statistically self-similar fractals. Zbl 0591.60005
Graf, Siegfried
55
1987
Exact Hausdorff dimension in random recursive constructions. Zbl 0625.60006
Mauldin, R. D.; Graf, S.; Williams, S. C.
8
1987
Random homeomorphisms. Zbl 0596.60005
Graf, S.; Mauldin, R. Daniel; Williams, S. C.
26
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
Problem section of Conf. on Measure Theory. Zbl 0549.28002
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
4
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
11
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
4
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
8
1976
On the existence of strong liftings in second countable topological spaces. Zbl 0304.46025
Graf, Siegfried
7
1975
all top 5

Cited by 670 Authors

42 Pagès, Gilles
28 Zhu, Sanguo
25 Roychowdhury, Mrinal Kanti
16 Luschgy, Harald
11 Graf, Siegfried
10 Pichler, Alois
9 Macheras, Nikolaos Demetrios
8 Bandt, Christoph
8 Hu, Dihe
8 Kreitmeier, Wolfgang
8 Mauldin, Richard Daniel
7 Dereich, Steffen
7 Strauss, Werner
6 Kesseböhmer, Marc
6 Matsuura, Shun
6 Musial, Kazimierz
6 Novak, Erich
6 Ritter, Klaus
6 Sagna, Abass
6 Troscheit, Sascha
5 Callegaro, Giorgia
5 Falconer, Kenneth J.
5 Fiorin, Lucio
5 Fraser, Jonathan MacDonald
5 Molchanov, Ilya S.
5 Patzschke, Norbert
5 Pflug, Georg Ch.
5 Staiger, Ludwig
5 Tarpey, Thaddeus
5 Tetenov, Andreĭ Viktorovich
5 Zähle, Martina
4 Barral, Julien
4 Fort, Jean-Claude
4 Hambly, Ben M.
4 Iacobelli, Mikaela
4 Jourdain, Benjamin
4 Kurata, Hiroshi
4 Mathew Karakkad, Sunil
4 Monticino, Michael G.
4 Mörters, Peter
4 Müller-Gronbach, Thomas
4 Olsen, Lars Ole Ronnow
4 Peres, Yuval
4 Pham, Huyên
4 Printems, Jacques
4 Römisch, Werner
4 Simon, Károly
4 Solomyak, Boris
4 Torra, Vicenç
4 Wilbertz, Benedikt
3 Aswathy, R. K.
3 Barnsley, Michael Fielding
3 Berger, Arno
3 Bonnans, Joseph Frédéric
3 Çömez, Doḡan
3 Dai, Meifeng
3 del Barrio, Eustasio
3 Elekes, Márton
3 Feng, De-Jun
3 Grasselli, Martino
3 Grekas, Stratos
3 Heitsch, Holger
3 Hutchinson, John Edward
3 Kamalutdinov, Kirill Glebovich
3 Kozma, Gady
3 Le Gouic, Thibaut
3 Li, Jinjun
3 Maharam Stone, Dorothy
3 Menozzi, Stéphane
3 Paris, Quentin
3 Patacchini, Francesco Saverio
3 Pronzato, Luc
3 Rams, Michał
3 Saracco, Jérôme
3 Sugeno, Michio
3 Wu, Min
3 Xi, Lifeng
3 Xu, Chuang
3 Zhou, Youming
2 Adamski, Wolfgang
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 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 Cen, Zhihao
2 Charlier, Isabelle
2 Christel, Thibault
...and 570 more Authors
all top 5

Cited in 215 Serials

30 Journal of Mathematical Analysis and Applications
24 Proceedings of the American Mathematical Society
16 Stochastic Processes and their Applications
14 Chaos, Solitons and Fractals
14 Advances in Mathematics
12 Israel Journal of Mathematics
11 Transactions of the American Mathematical Society
11 Probability Theory and Related Fields
10 Bernoulli
9 The Annals of Probability
8 Monatshefte für Mathematik
8 Journal of Theoretical Probability
8 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
7 Journal of Approximation Theory
7 Journal of Statistical Planning and Inference
7 Ergodic Theory and Dynamical Systems
7 Journal of Complexity
7 The Annals of Applied Probability
7 Fractals
7 Quantitative Finance
6 Mathematische Zeitschrift
6 Topology and its Applications
6 Wuhan University Journal of Natural Sciences (WUJNS)
5 Communications in Mathematical Physics
5 Statistics & Probability Letters
5 European Journal of Operational Research
5 Foundations of Computational Mathematics
4 Mathematical Proceedings of the Cambridge Philosophical Society
4 The Annals of Statistics
4 Journal of Functional Analysis
4 Journal of Multivariate Analysis
4 Mathematische Nachrichten
4 Advances in Applied Mathematics
4 Mathematical Programming. Series A. Series B
4 Calculus of Variations and Partial Differential Equations
4 Monte Carlo Methods and Applications
4 Discrete and Continuous Dynamical Systems
4 Electronic Journal of Statistics
4 Journal of Fractal Geometry
3 Advances in Applied Probability
3 The Mathematical Intelligencer
3 Fuzzy Sets and Systems
3 Mathematika
3 Memoirs of the American Mathematical Society
3 Real Analysis Exchange
3 Statistical Science
3 Forum Mathematicum
3 Annals of Operations Research
3 Statistical Papers
3 Mathematical Finance
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 Science China. Mathematics
2 Archive for Rational Mechanics and Analysis
2 Journal of Computational Physics
2 Nonlinearity
2 Studia Mathematica
2 Mathematics of Computation
2 Applied Mathematics and Computation
2 Automatica
2 Geometriae Dedicata
2 Journal of the American Statistical Association
2 Journal of Computational and Applied Mathematics
2 Journal of Soviet Mathematics
2 Mathematische Annalen
2 Mathematics of Operations Research
2 Numerische Mathematik
2 SIAM Journal on Control and Optimization
2 Siberian Mathematical Journal
2 Zeitschrift für Analysis und ihre Anwendungen
2 Acta Mathematica Hungarica
2 Acta Applicandae Mathematicae
2 Order
2 Constructive Approximation
2 Computational Statistics
2 Aequationes Mathematicae
2 Communications in Statistics. Theory and Methods
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 Communications of the Korean Mathematical Society
2 Acta Mathematica Sinica. English Series
2 Communications in Nonlinear Science and Numerical Simulation
2 Lobachevskii Journal of Mathematics
2 Qualitative Theory of Dynamical Systems
2 Dynamical Systems
2 Journal of Machine Learning Research (JMLR)
2 4OR
2 Kyoto Journal of Mathematics
1 Modern Physics Letters A
1 Biological Cybernetics
1 Bulletin of the Australian Mathematical Society
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
...and 115 more Serials
all top 5

Cited in 48 Fields

261 Measure and integration (28-XX)
244 Probability theory and stochastic processes (60-XX)
89 Statistics (62-XX)
65 Dynamical systems and ergodic theory (37-XX)
58 Numerical analysis (65-XX)
53 Information and communication theory, circuits (94-XX)
35 Operations research, mathematical programming (90-XX)
35 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
25 General topology (54-XX)
24 Calculus of variations and optimal control; optimization (49-XX)
22 Approximations and expansions (41-XX)
22 Functional analysis (46-XX)
19 Computer science (68-XX)
16 Partial differential equations (35-XX)
15 Harmonic analysis on Euclidean spaces (42-XX)
15 Convex and discrete geometry (52-XX)
12 Operator theory (47-XX)
11 Number theory (11-XX)
11 Real functions (26-XX)
11 Statistical mechanics, structure of matter (82-XX)
10 Systems theory; control (93-XX)
7 Mathematical logic and foundations (03-XX)
7 Differential geometry (53-XX)
7 Global analysis, analysis on manifolds (58-XX)
6 Combinatorics (05-XX)
6 Topological groups, Lie groups (22-XX)
6 Abstract harmonic analysis (43-XX)
5 Category theory; homological algebra (18-XX)
4 Group theory and generalizations (20-XX)
4 Potential theory (31-XX)
4 Fluid mechanics (76-XX)
3 General and overarching topics; collections (00-XX)
3 Order, lattices, ordered algebraic structures (06-XX)
3 Ordinary differential equations (34-XX)
3 Difference and functional equations (39-XX)
3 Mechanics of deformable solids (74-XX)
3 Biology and other natural sciences (92-XX)
2 Manifolds and cell complexes (57-XX)
2 Classical thermodynamics, heat transfer (80-XX)
1 History and biography (01-XX)
1 General algebraic systems (08-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Integral equations (45-XX)
1 Geometry (51-XX)
1 Algebraic topology (55-XX)
1 Mechanics of particles and systems (70-XX)
1 Quantum theory (81-XX)
1 Geophysics (86-XX)

Citations by Year

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