Publications by Pieter
Underlined papers are
in portable document format (pdf).
- An invariant-sum
characterization of Benford's law. J.
Appl. Prob. 34, 288-291 (1997)
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
- (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
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,
- (with K. Kawamura) On
the coordinate functions of Lévy's
dragon curve. Real Anal. Exchange 31, no. 1, 295-308
- Prophet regions for
discounted, uniformly bounded random variables. Stoch. Anal. Appl. 24, no. 3,
inequalities for i.i.d. random variables
with random arrival times. Sequential Anal. 26, no. 4,
- (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,
- Distribution of
the maxima of random Takagi functions. Acta
Math. Hungarica 121, no. 3,
- On a flexible class
of continuous functions with uniform local structure. J.
Math. Soc. Japan 61, no. 1, 237-262 (2009)
- (with R. D.
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
- 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,
- The finite
cardinalities of level sets of the Takagi function. J.
Math. Anal. Appl. 388 (2012), no. 2,
- How large are the level sets of the Takagi function? Monatsh. Math. 167 (2012),
- (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,
- 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,
- 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,
- (with J. Islas) A sharp lower bound
for choosing the maximum of an independent sequence. To appear in J. Applied Probab.; arXiv:1511.02211
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