Publications by Pieter
C. Allaart:
Underlined papers are
available
in portable document format (pdf).
- An invariant-sum
characterization of Benford's law. J.
Appl. Prob. 34, 288-291 (1997)
- Minimax
risk inequalities for the location-parameter classification problem.
J. Multivariate Anal. 66, no.2, 255-269 (1998)
- Bounds on the
non-convexity of ranges of vector measures with atoms. Contemp.
Math. 234, 1-11 (1999)
- A sharp non-convexity
bound for partition ranges of vector measures with atoms. J.
Math. Anal. Appl. 235, 326-348 (1999)
- Inequalities relating
maximal moments to other measures of dispersion. Statistica Neerlandica
54, no.3, 366-373 (2000)
- (with M. Monticino) Optimal stopping rules for directionally
reinforced processes. Adv. Appl. Prob. 33, no.2, 483-504
(2001)
- (with M. Monticino) Pseudoprophet
inequalities in average-optimal stopping. Sequential Anal. 22,
no. 3, 233-239 (2003).
- Moments of the mean of
Dubins-Freedman random probability
distributions. J. Theoretical Probab.
16, no. 2, 471-488 (2003)
- Optimal stopping rules
for correlated random walks with a discount. J. Appl. Prob. 41,
no. 2, 483-496 (2004)
- An application of
prophet regions to optimal stopping with a random number of
observations. Optimization 53, no. 4, 331-338 (2004)
- Stopping the maximum
of a correlated random walk, with cost for observation. J.
Appl. Prob. 41, no. 4, 998-1007 (2004)
- Prophet regions for
$[0,1]$-valued random variables with random
discounting. Stoch.
Anal. Appl. 23, no. 3, 491-509 (2005)
- (with K. Kawamura) Extreme
values of some continuous, nowhere differentiable functions. Math.
Proc. Camb. Phil. Soc. 140, no. 2,
269-295 (2006)
- (with K. Kawamura) On
the coordinate functions of Lévy's
dragon curve. Real Anal. Exchange 31, no. 1, 295-308
(2005/06)
- Prophet regions for
discounted, uniformly bounded random variables. Stoch. Anal. Appl. 24, no. 3,
531-554 (2006)
- Prophet
inequalities for i.i.d. random variables
with random arrival times. Sequential Anal. 26, no. 4,
403-413 (2007)
- (with K. Kawamura) Dimensions
of the coordinate functions of space-filling curves. J. Math.
Anal. Appl. 335, 1161-1176 (2007)
- (with M. Monticino) Optimal buy/sell strategies for
directionally reinforced processes. J. Appl. Prob. 45,
33-44 (2008)
- Distribution of
the maxima of random Takagi functions. Acta
Math. Hungarica 121, no. 3,
243-275 (2008)
- On a flexible class
of continuous functions with uniform local structure. J.
Math. Soc. Japan 61, no. 1, 237-262 (2009)
- (with R. D.
Mauldin) Injectivity
of the Dubins-Freedman construction of
random distributions. Contemp.
Math. 485, 1-11 (2009)
- A sharp ratio inequality for
optimal stopping when only relative record times are observed. Sequential Anal. 28, no. 4, 455-458
(2009)
- Optimal stopping
rules for American and Russian options in a correlated random walk
model. Stoch. Models 26,
no. 4, 594-616 (2010)
- A general
"bang-bang" principle for predicting the maximum of a random walk. J. Appl. Probab. 47, no. 4,
1072-1083 (2010); arXiv:0910.0545
- Predicting the supremum: optimality of "stop at once or not at
all" (To appear in J. Appl. Probab. (2012); arXiv:0912.0615)
- (with K. Kawamura)
The improper infinite derivatives of Takagi's nowhere differentiable
continuous function. J. Math.
Anal. Appl. 372, 656-665 (2010); arXiv:1002.2731
- An inequality for
sums of binary digits, with application to Takagi functions. J.
Math. Anal. Appl. 381 (2011), no. 2,
689–694; arXiv:1009.1308
- The finite
cardinalities of level sets of the Takagi function. J.
Math. Anal. Appl. 388 (2012), no. 2,
1117–1129; arXiv:1107.0712
- How large are the level sets of the Takagi function? Monatsh. Math. 167 (2012),
311-331; arXiv:1102.1616
- (with K. Kawamura)
The Takagi function: a survey. Real Anal. Exchange 37 (2011/12),
no. 1, 1-54; arXiv:1110.1691
- Level sets of signed Takagi
functions. Acta Math. Hungarica
141 (2013), no. 4, 339-352; arXiv:1209.6120
- Digital sum inequalities and
approximate convexity of Takagi-type functions. Math. Ineq. Appl. 17 (2014), no. 2,
679-691; arXiv:1208.2745
- On the level sets of the Takagi-van
der Waerden functions. J. Math.
Anal. Appl. 419, (2014), 1168-1180; arXiv:1312.2119
- Correction and strengthening of
``How large are the level sets of the Takagi function?", Monatsh. Math. 175 (2014), no. 2,
313-318; arXiv:1306.0167
- Hausdorff dimension of level sets
of generalized Takagi functions. Math.
Proc. Camb. Phil. Soc. 157 (2014), 253-278; arXiv:1301.4747
- The infinite derivatives of
Okamoto's function: an application of beta-expansions. J. Fractal Geom. 3 (2016), no. 1,
1-31; arXiv:1502.03374
- (with J. Islas) A sharp lower bound
for choosing the maximum of an independent sequence. J. Applied Probab. 53
(2016), no. 4, 1041-1051; arXiv:1511.02211
- On univoque and strongly univoque
sets. Adv. Math. 308
(2017), 575-598; arXiv:1601.04680v2
- Differentiability of a two-parameter family
of self-affine functions. J.
Math. Anal. Appl. 450 (2017), no. 2, 954–968; arXiv:1606.07838
- Differentiability and Holder spectra of a class of self-affine
functions. Adv. Math.
328 (2018), 1--39; arXiv:1707.07376v2
- (with S. Baker and D. Kong) Bifurcation
sets arising from non-integer base expansions. J. Fractal Geom. 6 (2019), no. 4,
301-341;
arXiv:1706.05190v4
- (with D. Kong) On the continuity of the
Hausdorff dimension of the univoque set. Adv. Math. 354 (2019), Article
106729, 24 pages; link to
arXiv
- An algebraic approach to entropy plateaus
in non-integer base expansions. Discrete
Contin. Dyn. Syst. A 39 (2019), no. 11, 6507--6522; link
to arXiv
- (with A. Allen) A random walk version of Robbins' problem: small
horizon. Math. Appl.
47 (2019), no. 2, 293-312; link
to arXiv
- The pointwise Holder spectrum of general self-affine functions on
an interval. J. Math. Anal.
Appl. 488 (2020), no. 2, Article 124096, 35 pages; link to arXiv
- (with R. Norouzi-Kandalan and K. Namuduri) Mobility Accelerates
Consensus-Building in Sensor Networks. IEEE Sensors Letters 4 (2020), no.
12, 1--4, doi:10.1109/LSENS.2020.3042127
- (with D. Kong) Relative bifurcation sets and the local dimension
of univoque bases. Ergodic
Theory Dynam. Systems 41 (2021), no. 8, 2241--2273; link to arXiv
- (with D. Kong) On the smallest base in which a number has a
unique expansion. Trans.
Amer. Math. Soc. 374 (2021), no. 9, 6201--6249; link to arXiv
- (with D. Kong) Density spectrum of Cantor measure. Submitted for
publication, 27 pages (2021); link to arXiv
- (with S. Jackson, T. Jones and D. Lambert) On the existence
of numbers with matching continued fraction and decimal expansions. Monatsh. Math. 202 (2023), no. 1, 1--30; link to arXiv (earlier version with a different title)
- (with D. Kong) Critical values for the beta-transformation with a hole at 0. Ergodic Theory Dynam. Systems 43 (2023), no. 6, 1785--1828; link to arXiv
- (with T. Jones) Box-counting dimension and differentiability of box-like statistically self-affine functions. J. Math. Anal. Appl. 521 (2023), no. 2, Article 126909; link to arXiv
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