**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

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