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Allaart, Pieter C.

Co-Author Distance
Author ID: allaart.pieter-c Recent zbMATH articles by "Allaart, Pieter C."
Published as: Allaart, Pieter C.; Allaart, Pieter; Allaart, P. C.
External Links: MGP
Documents Indexed: 55 Publications since 1997, including 2 Additional arXiv Preprints
Co-Authors: 9 Co-Authors with 23 Joint Publications
134 Co-Co-Authors
all top 5

Co-Authors

32 single-authored
7 Kawamura, Kiko
7 Kong, Derong
3 Jones, Taylor
3 Monticino, Michael G.
1 Allen, Andrew S.
1 Baker, Simon
1 Islas, José A.
1 Lambert, David E.
1 Mauldin, Richard Daniel
all top 5

Serials

9 Journal of Mathematical Analysis and Applications
7 Journal of Applied Probability
4 Real Analysis Exchange
3 Advances in Mathematics
3 Monatshefte für Mathematik
3 Sequential Analysis
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Ergodic Theory and Dynamical Systems
2 Stochastic Analysis and Applications
2 Acta Mathematica Hungarica
2 Journal of Fractal Geometry
1 Advances in Applied Probability
1 Nonlinearity
1 Journal of the Mathematical Society of Japan
1 Journal of Multivariate Analysis
1 Statistica Neerlandica
1 Transactions of the American Mathematical Society
1 Optimization
1 Journal of Theoretical Probability
1 Discrete and Continuous Dynamical Systems
1 Mathematical Inequalities & Applications
1 Stochastic Models
1 Mathematica Applicanda
all top 5

Fields

25 Probability theory and stochastic processes (60-XX)
22 Measure and integration (28-XX)
21 Real functions (26-XX)
10 Dynamical systems and ergodic theory (37-XX)
9 Number theory (11-XX)
9 Statistics (62-XX)
3 General topology (54-XX)
3 Computer science (68-XX)
1 Difference and functional equations (39-XX)
1 Functional analysis (46-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

38 Publications have been cited 227 times in 147 Documents Cited by ▼ Year ▼
The Takagi function: a survey. Zbl 1248.26007
Allaart, Pieter C.; Kawamura, Kiko
57
2012
The improper infinite derivatives of Takagi’s nowhere-differentiable function. Zbl 1202.26009
Allaart, Pieter C.; Kawamura, Kiko
17
2010
Extreme values of some continuous nowhere differentiable functions. Zbl 1086.26004
Allaart, Pieter C.; Kawamura, Kiko
14
2006
On the continuity of the Hausdorff dimension of the univoque set. Zbl 1473.11015
Allaart, Pieter; Kong, Derong
11
2019
On univoque and strongly univoque sets. Zbl 1362.11074
Allaart, Pieter C.
8
2017
The infinite derivatives of Okamoto’s self-affine functions: an application of \(\beta\)-expansions. Zbl 1350.26006
Allaart, Pieter C.
7
2016
Optimal stopping rules for correlated random walks with a discount. Zbl 1071.60026
Allaart, Pieter
7
2004
A general ‘bang-bang’ principle for predicting the maximum of a random walk. Zbl 1225.60068
Allaart, Pieter
7
2010
Relative bifurcation sets and the local dimension of univoque bases. Zbl 1475.11014
Allaart, Pieter; Kong, Derong
7
2021
Optimal stopping rules for directionally reinforced processes. Zbl 0988.60039
Allaart, Pieter; Monticino, Michael
7
2001
Bifurcation sets arising from non-integer base expansions. Zbl 1435.11102
Allaart, Pieter; Baker, Simon; Kong, Derong
6
2019
How large are the level sets of the Takagi function? Zbl 1256.26002
Allaart, Pieter C.
6
2012
An invariant-sum characterization of Benford’s law. Zbl 0874.60016
Allaart, Pieter C.
6
1997
Differentiability and Hölder spectra of a class of self-affine functions. Zbl 1391.28004
Allaart, Pieter C.
6
2018
The finite cardinalities of level sets of the Takagi function. Zbl 1234.26007
Allaart, Pieter C.
5
2012
On a flexible class of continuous functions with uniform local structure. Zbl 1161.26003
Allaart, Pieter C.
5
2009
Optimal buy/sell rules for correlated random walks. Zbl 1136.60028
Allaart, Pieter; Monticino, Michael
5
2008
Distribution of the maxima of random Takagi functions. Zbl 1199.28011
Allaart, P. C.
5
2008
An inequality for sums of binary digits, with application to Takagi functions. Zbl 1223.26018
Allaart, Pieter C.
5
2011
An algebraic approach to entropy plateaus in non-integer base expansions. Zbl 1473.11014
Allaart, Pieter C.
4
2019
On the level sets of the Takagi-van der Waerden functions. Zbl 1349.26010
Allaart, Pieter C.
3
2014
Level sets of signed Takagi functions. Zbl 1313.26008
Allaart, P. C.
3
2013
Pseudo-prophet inequalities in average-optimal stopping. Zbl 1125.60304
Allaart, Pieter; Monticino, Michael
3
2003
Differentiability of a two-parameter family of self-affine functions. Zbl 1373.28005
Allaart, Pieter C.
3
2017
On the smallest base in which a number has a unique expansion. Zbl 1491.11010
Allaart, Pieter; Kong, Derong
3
2021
An application of prophet regions to optimal stopping with a random number of observations. Zbl 1075.60036
Allaart, Pieter C.
2
2004
Dimensions of the coordinate functions of space-filling curves. Zbl 1125.54017
Allaart, Pieter C.; Kawamura, Kiko
2
2007
Prophet inequalities for I.I.D. random variables with random arrival times. Zbl 1136.60027
Allaart, Pieter C.
2
2007
Critical values for the \(\beta\)-transformation with a hole at \(0\). Zbl 1518.37013
Allaart, Pieter; Kong, Derong
2
2023
Digital sum inequalities and approximate convexity of Takagi-type functions. Zbl 1358.11021
Allaart, Pieter C.
1
2014
Prophet regions for independent \([0,1]\)-valued random variables with random discounting. Zbl 1079.60042
Allaart, Pieter C.
1
2005
Moments of the mean of Dubins-Freedman random probability distributions. Zbl 1025.60006
Allaart, Pieter
1
2003
Stopping the maximum of a correlated random walk, with cost for observation. Zbl 1068.60060
Allaart, Pieter
1
2004
Bounds on the non-convexity of ranges of vector measures with atoms. Zbl 0937.28010
Allaart, Pieter C.
1
1999
A sharp nonconvexity bound for partition ranges of vector measures with atoms. Zbl 0955.28005
Allaart, Pieter C.
1
1999
A sharp ratio inequality for optimal stopping when only record times are observed. Zbl 1183.62137
Allaart, Pieter C.
1
2009
A random walk version of Robbins’ problem: small horizon. Zbl 1463.60062
Allaart, Pieter; Allen, Andrew
1
2019
A sharp lower bound for choosing the maximum of an independent sequence. Zbl 1355.60055
Allaart, Pieter C.; Islas, José A.
1
2016
Critical values for the \(\beta\)-transformation with a hole at \(0\). Zbl 1518.37013
Allaart, Pieter; Kong, Derong
2
2023
Relative bifurcation sets and the local dimension of univoque bases. Zbl 1475.11014
Allaart, Pieter; Kong, Derong
7
2021
On the smallest base in which a number has a unique expansion. Zbl 1491.11010
Allaart, Pieter; Kong, Derong
3
2021
On the continuity of the Hausdorff dimension of the univoque set. Zbl 1473.11015
Allaart, Pieter; Kong, Derong
11
2019
Bifurcation sets arising from non-integer base expansions. Zbl 1435.11102
Allaart, Pieter; Baker, Simon; Kong, Derong
6
2019
An algebraic approach to entropy plateaus in non-integer base expansions. Zbl 1473.11014
Allaart, Pieter C.
4
2019
A random walk version of Robbins’ problem: small horizon. Zbl 1463.60062
Allaart, Pieter; Allen, Andrew
1
2019
Differentiability and Hölder spectra of a class of self-affine functions. Zbl 1391.28004
Allaart, Pieter C.
6
2018
On univoque and strongly univoque sets. Zbl 1362.11074
Allaart, Pieter C.
8
2017
Differentiability of a two-parameter family of self-affine functions. Zbl 1373.28005
Allaart, Pieter C.
3
2017
The infinite derivatives of Okamoto’s self-affine functions: an application of \(\beta\)-expansions. Zbl 1350.26006
Allaart, Pieter C.
7
2016
A sharp lower bound for choosing the maximum of an independent sequence. Zbl 1355.60055
Allaart, Pieter C.; Islas, José A.
1
2016
On the level sets of the Takagi-van der Waerden functions. Zbl 1349.26010
Allaart, Pieter C.
3
2014
Digital sum inequalities and approximate convexity of Takagi-type functions. Zbl 1358.11021
Allaart, Pieter C.
1
2014
Level sets of signed Takagi functions. Zbl 1313.26008
Allaart, P. C.
3
2013
The Takagi function: a survey. Zbl 1248.26007
Allaart, Pieter C.; Kawamura, Kiko
57
2012
How large are the level sets of the Takagi function? Zbl 1256.26002
Allaart, Pieter C.
6
2012
The finite cardinalities of level sets of the Takagi function. Zbl 1234.26007
Allaart, Pieter C.
5
2012
An inequality for sums of binary digits, with application to Takagi functions. Zbl 1223.26018
Allaart, Pieter C.
5
2011
The improper infinite derivatives of Takagi’s nowhere-differentiable function. Zbl 1202.26009
Allaart, Pieter C.; Kawamura, Kiko
17
2010
A general ‘bang-bang’ principle for predicting the maximum of a random walk. Zbl 1225.60068
Allaart, Pieter
7
2010
On a flexible class of continuous functions with uniform local structure. Zbl 1161.26003
Allaart, Pieter C.
5
2009
A sharp ratio inequality for optimal stopping when only record times are observed. Zbl 1183.62137
Allaart, Pieter C.
1
2009
Optimal buy/sell rules for correlated random walks. Zbl 1136.60028
Allaart, Pieter; Monticino, Michael
5
2008
Distribution of the maxima of random Takagi functions. Zbl 1199.28011
Allaart, P. C.
5
2008
Dimensions of the coordinate functions of space-filling curves. Zbl 1125.54017
Allaart, Pieter C.; Kawamura, Kiko
2
2007
Prophet inequalities for I.I.D. random variables with random arrival times. Zbl 1136.60027
Allaart, Pieter C.
2
2007
Extreme values of some continuous nowhere differentiable functions. Zbl 1086.26004
Allaart, Pieter C.; Kawamura, Kiko
14
2006
Prophet regions for independent \([0,1]\)-valued random variables with random discounting. Zbl 1079.60042
Allaart, Pieter C.
1
2005
Optimal stopping rules for correlated random walks with a discount. Zbl 1071.60026
Allaart, Pieter
7
2004
An application of prophet regions to optimal stopping with a random number of observations. Zbl 1075.60036
Allaart, Pieter C.
2
2004
Stopping the maximum of a correlated random walk, with cost for observation. Zbl 1068.60060
Allaart, Pieter
1
2004
Pseudo-prophet inequalities in average-optimal stopping. Zbl 1125.60304
Allaart, Pieter; Monticino, Michael
3
2003
Moments of the mean of Dubins-Freedman random probability distributions. Zbl 1025.60006
Allaart, Pieter
1
2003
Optimal stopping rules for directionally reinforced processes. Zbl 0988.60039
Allaart, Pieter; Monticino, Michael
7
2001
Bounds on the non-convexity of ranges of vector measures with atoms. Zbl 0937.28010
Allaart, Pieter C.
1
1999
A sharp nonconvexity bound for partition ranges of vector measures with atoms. Zbl 0955.28005
Allaart, Pieter C.
1
1999
An invariant-sum characterization of Benford’s law. Zbl 0874.60016
Allaart, Pieter C.
6
1997
all cited Publications top 5 cited Publications
all top 5

Cited by 181 Authors

28 Allaart, Pieter C.
11 Kong, Derong
7 Ferrera, Juan
7 Gomez Gil, Javier
5 Schied, Alexander
4 Fujita, Yasuhiro
4 Galkin, Oleg Evgen’evich
4 Galkina, Svetlana Yur’evna
4 Komornik, Vilmos
4 Li, Wenxia
4 Llorente, Jesús
4 Minabutdinov, A. R.
4 Sumi, Hiroki
4 Yamaguchi, Norikazu
3 Berger, Arno
3 Fernández-Sánchez, Juan
3 Hamamuki, Nao
3 Hill, Theodore Preston
3 Jaerisch, Johannes
3 Kawamura, Kiko
3 Zou, Yuru
2 Baker, Simon
2 Bárány, Balázs
2 Bernal-Gonzàlez, Luis
2 De Amo, Enrique
2 Diaz Carrillo, Manuel
2 Ghosh, Arka Prasanna
2 Han, Xiyue
2 Loreti, Paola
2 Lu, Fan
2 Maddock, Zachary
2 Mihailescu, Eugen
2 Mishura, Yuliya Stepanivna
2 Okamura, Kazuki
2 Osękowski, Adam
2 Rams, Michał
2 Roitershtein, Alexander
2 Seoane-Sepúlveda, Juan Benigno
2 Siconolfi, Antonio
2 Simon, Károly
2 Van Schaik, Kees
2 Vorob’ev, A. L.
2 Yam, Sheung Chi Phillip
2 Yung, Siu Pang
2 Zhang, Zhenyuan
1 Agadzhanov, A. N.
1 Alcaraz Barrera, Rafael
1 Allouche, Jean-Paul Simon
1 Appell, Jürgen
1 Araújo, Gustavo da Silva
1 Arthur, C.
1 Barabesi, Lucio
1 Baurdoux, Erik Jan
1 Ben Slimane, Mourad
1 Bhouri, Imen
1 Bruss, Franz Thomas
1 Calka, Pierre
1 Carminati, Carlo
1 Carvajal Pinto, Mónica B.
1 Cerasa, Andrea
1 Cerioli, Andrea
1 Coronado, Tomás M.
1 Correa, José R.
1 Costa Júnior, Fernando
1 Couch, PJ
1 Dalaklis, Nathan
1 Dall’Aglio, Marco
1 Daniel, B. D.
1 Daubechies, Ingrid
1 de Vries, Martijn
1 Demichel, Yann
1 DeVore, Ronald A.
1 Ding, Yiming
1 Dougall, Rhiannon
1 Dubuc, Serge
1 Dumas, Philippe
1 Fischer, Mareike
1 Foncea, Patricio
1 Foucart, Simon
1 Gaitán, Alejandra
1 García Macías, Gonzalo
1 Georgiou, Nicholas
1 Gordienko, Evgueni I.
1 Grau, José María
1 Hanin, B.
1 Herbst, Lina
1 Hoeksma, Ruben
1 Hoseana, Jonathan
1 Hrušák, Michael
1 Huang, Yan
1 Hürlimann, Werner
1 Hwang, Hsien-Kuei
1 Janson, Svante
1 Jiang, Kan
1 Jones, Taylor
1 Kalle, Charlene
1 Katzourakis, Nikolaos I.
1 Khosravani, Azar N.
1 Konno, Norio
1 Kosmala, Tomasz
...and 81 more Authors
all top 5

Cited in 81 Serials

14 Journal of Mathematical Analysis and Applications
8 Monatshefte für Mathematik
6 Acta Mathematica Hungarica
5 Advances in Mathematics
5 Journal of Applied Probability
5 Ergodic Theory and Dynamical Systems
4 Journal of Mathematical Sciences (New York)
3 Nonlinearity
3 Journal of Number Theory
3 Proceedings of the American Mathematical Society
3 Real Analysis Exchange
3 Journal of Theoretical Probability
3 Journal of Fractal Geometry
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Moscow University Mathematics Bulletin
2 International Journal of Mathematics and Mathematical Sciences
2 Journal of Functional Analysis
2 Transactions of the American Mathematical Society
2 Topology and its Applications
2 Advances in Applied Mathematics
2 Stochastic Analysis and Applications
2 Acta Applicandae Mathematicae
2 Fractals
2 Journal of Convex Analysis
2 Stochastic Models
2 Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
1 Advances in Applied Probability
1 Analysis Mathematica
1 Communications in Mathematical Physics
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Mathematical Biology
1 Journal of Statistical Physics
1 Mathematische Semesterberichte
1 Mathematics Magazine
1 Acta Arithmetica
1 Applied Mathematics and Computation
1 Functional Analysis and its Applications
1 Journal of the American Statistical Association
1 Kybernetika
1 Mathematische Annalen
1 Mathematics of Operations Research
1 Michigan Mathematical Journal
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Proceedings of the Japan Academy. Series A
1 Theoretical Computer Science
1 Statistics & Probability Letters
1 Acta Mathematicae Applicatae Sinica. English Series
1 Optimization
1 Sequential Analysis
1 Constructive Approximation
1 SIAM Journal on Discrete Mathematics
1 Japan Journal of Industrial and Applied Mathematics
1 Aequationes Mathematicae
1 Applied Mathematical Modelling
1 Stochastic Processes and their Applications
1 Bulletin of the American Mathematical Society. New Series
1 Expositiones Mathematicae
1 Theory of Probability and Mathematical Statistics
1 Sbornik: Mathematics
1 Annales Academiae Scientiarum Fennicae. Mathematica
1 Doklady Mathematics
1 Theory of Computing Systems
1 Abstract and Applied Analysis
1 Positivity
1 Mathematical Methods of Operations Research
1 Fractional Calculus & Applied Analysis
1 Revista Matemática Complutense
1 Journal of Integer Sequences
1 Statistical Inference for Stochastic Processes
1 Probability in the Engineering and Informational Sciences
1 Nonlinear Analysis. Modelling and Control
1 Miscelánea Matemática
1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
1 Oberwolfach Reports
1 Set-Valued and Variational Analysis
1 Probability Surveys
1 S\(\vec{\text{e}}\)MA Journal
1 Communications in Mathematics
1 Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki
1 Journal of Computational Dynamics
1 SN Partial Differential Equations and Applications
all top 5

Cited in 29 Fields

65 Real functions (26-XX)
55 Measure and integration (28-XX)
42 Probability theory and stochastic processes (60-XX)
34 Dynamical systems and ergodic theory (37-XX)
31 Number theory (11-XX)
14 Statistics (62-XX)
14 Computer science (68-XX)
8 Difference and functional equations (39-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Functional analysis (46-XX)
4 Combinatorics (05-XX)
4 Partial differential equations (35-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
4 General topology (54-XX)
4 Operations research, mathematical programming (90-XX)
3 Operator theory (47-XX)
3 Numerical analysis (65-XX)
2 Mathematical logic and foundations (03-XX)
2 Approximations and expansions (41-XX)
2 Statistical mechanics, structure of matter (82-XX)
2 Biology and other natural sciences (92-XX)
1 General and overarching topics; collections (00-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Topological groups, Lie groups (22-XX)
1 Functions of a complex variable (30-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Mechanics of particles and systems (70-XX)
1 Mechanics of deformable solids (74-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year