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Allaart, Pieter C.

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 Author ID: allaart.pieter-c Published as: Allaart, Pieter C.; Allaart, Pieter; Allaart, P. C. External Links: MGP
 Documents Indexed: 49 Publications since 1997
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Co-Authors

 32 single-authored 7 Kawamura, Kiko 4 Kong, Derong 3 Monticino, Michael G. 1 Allen, Andrew S. 1 Baker, Simon 1 Islas, José A. 1 Mauldin, Richard Daniel
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Serials

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

 24 Probability theory and stochastic processes (60-XX) 17 Real functions (26-XX) 16 Measure and integration (28-XX) 9 Statistics (62-XX) 8 Number theory (11-XX) 7 Dynamical systems and ergodic theory (37-XX) 3 General topology (54-XX) 2 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)

Citations contained in zbMATH Open

34 Publications have been cited 162 times in 103 Documents Cited by Year
The Takagi function: a survey. Zbl 1248.26007
Allaart, Pieter C.; Kawamura, Kiko
2012
The improper infinite derivatives of Takagi’s nowhere-differentiable function. Zbl 1202.26009
Allaart, Pieter C.; Kawamura, Kiko
2010
Extreme values of some continuous nowhere differentiable functions. Zbl 1086.26004
Allaart, Pieter C.; Kawamura, Kiko
2006
Optimal stopping rules for correlated random walks with a discount. Zbl 1071.60026
Allaart, Pieter
2004
Optimal stopping rules for directionally reinforced processes. Zbl 0988.60039
Allaart, Pieter; Monticino, Michael
2001
On univoque and strongly univoque sets. Zbl 1362.11074
Allaart, Pieter C.
2017
How large are the level sets of the Takagi function? Zbl 1256.26002
Allaart, Pieter C.
2012
The finite cardinalities of level sets of the Takagi function. Zbl 1234.26007
Allaart, Pieter C.
2012
On the continuity of the Hausdorff dimension of the univoque set. Zbl 07103850
Allaart, Pieter; Kong, Derong
2019
A general ‘bang-bang’ principle for predicting the maximum of a random walk. Zbl 1225.60068
Allaart, Pieter
2010
The infinite derivatives of Okamoto’s self-affine functions: an application of $$\beta$$-expansions. Zbl 1350.26006
Allaart, Pieter C.
2016
An invariant-sum characterization of Benford’s law. Zbl 0874.60016
Allaart, Pieter C.
1997
Optimal buy/sell rules for correlated random walks. Zbl 1136.60028
Allaart, Pieter; Monticino, Michael
2008
On a flexible class of continuous functions with uniform local structure. Zbl 1161.26003
Allaart, Pieter C.
2009
Distribution of the maxima of random Takagi functions. Zbl 1199.28011
Allaart, P. C.
2008
An inequality for sums of binary digits, with application to Takagi functions. Zbl 1223.26018
Allaart, Pieter C.
2011
Bifurcation sets arising from non-integer base expansions. Zbl 1435.11102
Allaart, Pieter; Baker, Simon; Kong, Derong
2019
Level sets of signed Takagi functions. Zbl 1313.26008
Allaart, P. C.
2013
Differentiability and Hölder spectra of a class of self-affine functions. Zbl 1391.28004
Allaart, Pieter C.
2018
Differentiability of a two-parameter family of self-affine functions. Zbl 1373.28005
Allaart, Pieter C.
2017
Pseudo-prophet inequalities in average-optimal stopping. Zbl 1125.60304
Allaart, Pieter; Monticino, Michael
2003
Dimensions of the coordinate functions of space-filling curves. Zbl 1125.54017
Allaart, Pieter C.; Kawamura, Kiko
2007
An algebraic approach to entropy plateaus in non-integer base expansions. Zbl 07107987
Allaart, Pieter C.
2019
An application of prophet regions to optimal stopping with a random number of observations. Zbl 1075.60036
Allaart, Pieter C.
2004
A sharp nonconvexity bound for partition ranges of vector measures with atoms. Zbl 0955.28005
Allaart, Pieter C.
1999
Prophet inequalities for I.I.D. random variables with random arrival times. Zbl 1136.60027
Allaart, Pieter C.
2007
A sharp ratio inequality for optimal stopping when only record times are observed. Zbl 1183.62137
Allaart, Pieter C.
2009
A sharp lower bound for choosing the maximum of an independent sequence. Zbl 1355.60055
Allaart, Pieter C.; Islas, José A.
2016
Bounds on the non-convexity of ranges of vector measures with atoms. Zbl 0937.28010
Allaart, Pieter C.
1999
Prophet regions for independent $$[0,1]$$-valued random variables with random discounting. Zbl 1079.60042
Allaart, Pieter C.
2005
Stopping the maximum of a correlated random walk, with cost for observation. Zbl 1068.60060
Allaart, Pieter
2004
On the level sets of the Takagi-van der Waerden functions. Zbl 1349.26010
Allaart, Pieter C.
2014
Moments of the mean of Dubins-Freedman random probability distributions. Zbl 1025.60006
Allaart, Pieter
2003
Relative bifurcation sets and the local dimension of univoque bases. Zbl 07371039
Allaart, Pieter; Kong, Derong
2021
Relative bifurcation sets and the local dimension of univoque bases. Zbl 07371039
Allaart, Pieter; Kong, Derong
2021
On the continuity of the Hausdorff dimension of the univoque set. Zbl 07103850
Allaart, Pieter; Kong, Derong
2019
Bifurcation sets arising from non-integer base expansions. Zbl 1435.11102
Allaart, Pieter; Baker, Simon; Kong, Derong
2019
An algebraic approach to entropy plateaus in non-integer base expansions. Zbl 07107987
Allaart, Pieter C.
2019
Differentiability and Hölder spectra of a class of self-affine functions. Zbl 1391.28004
Allaart, Pieter C.
2018
On univoque and strongly univoque sets. Zbl 1362.11074
Allaart, Pieter C.
2017
Differentiability of a two-parameter family of self-affine functions. Zbl 1373.28005
Allaart, Pieter C.
2017
The infinite derivatives of Okamoto’s self-affine functions: an application of $$\beta$$-expansions. Zbl 1350.26006
Allaart, Pieter C.
2016
A sharp lower bound for choosing the maximum of an independent sequence. Zbl 1355.60055
Allaart, Pieter C.; Islas, José A.
2016
On the level sets of the Takagi-van der Waerden functions. Zbl 1349.26010
Allaart, Pieter C.
2014
Level sets of signed Takagi functions. Zbl 1313.26008
Allaart, P. C.
2013
The Takagi function: a survey. Zbl 1248.26007
Allaart, Pieter C.; Kawamura, Kiko
2012
How large are the level sets of the Takagi function? Zbl 1256.26002
Allaart, Pieter C.
2012
The finite cardinalities of level sets of the Takagi function. Zbl 1234.26007
Allaart, Pieter C.
2012
An inequality for sums of binary digits, with application to Takagi functions. Zbl 1223.26018
Allaart, Pieter C.
2011
The improper infinite derivatives of Takagi’s nowhere-differentiable function. Zbl 1202.26009
Allaart, Pieter C.; Kawamura, Kiko
2010
A general ‘bang-bang’ principle for predicting the maximum of a random walk. Zbl 1225.60068
Allaart, Pieter
2010
On a flexible class of continuous functions with uniform local structure. Zbl 1161.26003
Allaart, Pieter C.
2009
A sharp ratio inequality for optimal stopping when only record times are observed. Zbl 1183.62137
Allaart, Pieter C.
2009
Optimal buy/sell rules for correlated random walks. Zbl 1136.60028
Allaart, Pieter; Monticino, Michael
2008
Distribution of the maxima of random Takagi functions. Zbl 1199.28011
Allaart, P. C.
2008
Dimensions of the coordinate functions of space-filling curves. Zbl 1125.54017
Allaart, Pieter C.; Kawamura, Kiko
2007
Prophet inequalities for I.I.D. random variables with random arrival times. Zbl 1136.60027
Allaart, Pieter C.
2007
Extreme values of some continuous nowhere differentiable functions. Zbl 1086.26004
Allaart, Pieter C.; Kawamura, Kiko
2006
Prophet regions for independent $$[0,1]$$-valued random variables with random discounting. Zbl 1079.60042
Allaart, Pieter C.
2005
Optimal stopping rules for correlated random walks with a discount. Zbl 1071.60026
Allaart, Pieter
2004
An application of prophet regions to optimal stopping with a random number of observations. Zbl 1075.60036
Allaart, Pieter C.
2004
Stopping the maximum of a correlated random walk, with cost for observation. Zbl 1068.60060
Allaart, Pieter
2004
Pseudo-prophet inequalities in average-optimal stopping. Zbl 1125.60304
Allaart, Pieter; Monticino, Michael
2003
Moments of the mean of Dubins-Freedman random probability distributions. Zbl 1025.60006
Allaart, Pieter
2003
Optimal stopping rules for directionally reinforced processes. Zbl 0988.60039
Allaart, Pieter; Monticino, Michael
2001
A sharp nonconvexity bound for partition ranges of vector measures with atoms. Zbl 0955.28005
Allaart, Pieter C.
1999
Bounds on the non-convexity of ranges of vector measures with atoms. Zbl 0937.28010
Allaart, Pieter C.
1999
An invariant-sum characterization of Benford’s law. Zbl 0874.60016
Allaart, Pieter C.
1997
all top 5

Cited by 122 Authors

 24 Allaart, Pieter C. 6 Kong, Derong 4 Minabutdinov, A. R. 4 Sumi, Hiroki 3 Berger, Arno 3 Ferrera, Juan 3 Gomez Gil, Javier 3 Hill, Theodore Preston 3 Jaerisch, Johannes 3 Li, Wenxia 3 Schied, Alexander 2 De Amo, Enrique 2 Diaz Carrillo, Manuel 2 Fernández-Sánchez, Juan 2 Fujita, Yasuhiro 2 Ghosh, Arka Prasanna 2 Hamamuki, Nao 2 Kawamura, Kiko 2 Lu, Fan 2 Maddock, Zachary 2 Mishura, Yuliya Stepanivna 2 Osękowski, Adam 2 Roitershtein, Alexander 2 Vorob’ev, A. L. 2 Yam, Sheung Chi Phillip 2 Yamaguchi, Norikazu 2 Yung, Siu Pang 2 Zhou, Wei 1 Agadzhanov, A. N. 1 Alcaraz Barrera, Rafael 1 Appell, Jürgen M. 1 Arthur, C. 1 Bárány, Balázs 1 Baurdoux, Erik Jan 1 Ben Slimane, Mourad 1 Bernal-Gonzàlez, Luis 1 Bhouri, Imen 1 Calka, Pierre 1 Coronado, Tomás M. 1 Couch, PJ 1 Dall’Aglio, Marco 1 Daniel, B. D. 1 Demichel, Yann 1 Dougall, Rhiannon 1 Dubuc, Serge 1 Dumas, Philippe 1 Fischer, Mareike 1 Gaitán, Alejandra 1 Galkin, Oleg Evgen’evich 1 Galkina, Svetlana Yur’evna 1 Georgiou, Nicholas 1 Gordienko, Evgueni I. 1 Grau, José María 1 Herbst, Lina 1 Hoseana, Jonathan 1 Hrušák, Michael 1 Hürlimann, Werner 1 Kalle, Charlene 1 Katzourakis, Nikolaos I. 1 Khosravani, Azar N. 1 Konno, Norio 1 Kwela, Adam 1 Lagarias, Jeffrey C. 1 Lev, Vsevolod F. 1 Li, Haixiong 1 Lijoi, Antonio 1 Liu, Chuntai 1 Llorente, Jesús 1 Lodkin, A. A. 1 Makó, Judit 1 Makogin, Vitalii 1 Manaev, I. E. 1 Mátrai, Tamás 1 McNicholl, Timothy H. 1 Mélot, Clothilde 1 Mena, Ramsés H. 1 Mihailescu, Eugen Gh. 1 Monticino, Michael G. 1 Morrison, Kent E. 1 Nekvinda, Aleš 1 Noren, Steven 1 Novikov, Andreĭ Alekseevich 1 Okamura, Kazuki 1 Osaka, Shoto 1 Pellegrino, Daniel Marinho 1 Prünster, Igor 1 Rams, Michał 1 Rasinariu, Constantin 1 Rastegar, Reza 1 Redtwitz, D. A. 1 Reinwand, Simon 1 Rosselló, Francesc 1 Sáenz, Ricardo A. 1 Seoane-Sepúlveda, Juan Benigno 1 Sheipak, Igor A. 1 Siconolfi, Antonio 1 Simon, Károly 1 Steinerberger, Stefan 1 Tabor, Jacek 1 Tabor, Józef ...and 22 more Authors
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Cited in 60 Serials

 13 Journal of Mathematical Analysis and Applications 7 Monatshefte für Mathematik 5 Advances in Mathematics 5 Journal of Applied Probability 4 Acta Mathematica Hungarica 4 Journal of Mathematical Sciences (New York) 3 Ergodic Theory and Dynamical Systems 2 Moscow University Mathematics Bulletin 2 International Journal of Mathematics and Mathematical Sciences 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Stochastic Analysis and Applications 2 Acta Applicandae Mathematicae 2 Journal of Theoretical Probability 2 Fractals 2 Stochastic Models 1 Communications in Mathematical Physics 1 Journal of Mathematical Biology 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematische Semesterberichte 1 Nonlinearity 1 Mathematics Magazine 1 Acta Arithmetica 1 Applied Mathematics and Computation 1 Functional Analysis and its Applications 1 Kybernetika 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Japan Academy. Series A 1 Real Analysis Exchange 1 Theoretical Computer Science 1 Topology and its Applications 1 Advances in Applied Mathematics 1 Statistics & Probability Letters 1 Acta Mathematicae Applicatae Sinica. English Series 1 Optimization 1 Sequential Analysis 1 SIAM Journal on Discrete Mathematics 1 Japan Journal of Industrial and Applied Mathematics 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 Journal of Convex Analysis 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 Fractional Calculus & Applied Analysis 1 Revista Matemática Complutense 1 Statistical Inference for Stochastic Processes 1 Probability in the Engineering and Informational Sciences 1 Nonlinear Analysis. Modelling and Control 1 Miscelánea Matemática 1 Probability Surveys 1 S$$\vec{\text{e}}$$MA Journal 1 Journal of Computational Dynamics 1 Journal of Fractal Geometry 1 SN Partial Differential Equations and Applications
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Cited in 24 Fields

 43 Real functions (26-XX) 34 Measure and integration (28-XX) 34 Probability theory and stochastic processes (60-XX) 19 Dynamical systems and ergodic theory (37-XX) 16 Number theory (11-XX) 12 Statistics (62-XX) 6 Computer science (68-XX) 5 Difference and functional equations (39-XX) 4 General topology (54-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Combinatorics (05-XX) 3 Functional analysis (46-XX) 3 Numerical analysis (65-XX) 2 Mathematical logic and foundations (03-XX) 2 Partial differential equations (35-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Operations research, mathematical programming (90-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)