Publications by Pieter C. Allaart:

Underlined papers are available in portable document format (pdf).

  1. An invariant-sum characterization of Benford's law. J. Appl. Prob. 34, 288-291 (1997)
  2. Minimax risk inequalities for the location-parameter classification problem. J. Multivariate Anal. 66, no.2, 255-269 (1998)
  3. Bounds on the non-convexity of ranges of vector measures with atoms. Contemp. Math. 234, 1-11 (1999)
  4. A sharp non-convexity bound for partition ranges of vector measures with atoms. J. Math. Anal. Appl. 235, 326-348 (1999)
  5. Inequalities relating maximal moments to other measures of dispersion. Statistica Neerlandica 54, no.3, 366-373 (2000)
  6. (with M. Monticino) Optimal stopping rules for directionally reinforced processes. Adv. Appl. Prob. 33, no.2, 483-504 (2001)
  7. (with M. Monticino) Pseudoprophet inequalities in average-optimal stopping. Sequential Anal. 22, no. 3, 233-239 (2003).
  8. Moments of the mean of Dubins-Freedman random probability distributions. J. Theoretical Probab. 16, no. 2, 471-488 (2003)
  9. Optimal stopping rules for correlated random walks with a discount. J. Appl. Prob. 41, no. 2, 483-496 (2004)
  10. An application of prophet regions to optimal stopping with a random number of observations.  Optimization 53, no. 4, 331-338 (2004)
  11. Stopping the maximum of a correlated random walk, with cost for observation. J. Appl. Prob. 41, no. 4, 998-1007 (2004)
  12. Prophet regions for $[0,1]$-valued random variables with random discounting.  Stoch. Anal. Appl. 23, no. 3, 491-509 (2005)
  13. (with K. Kawamura) Extreme values of some continuous, nowhere differentiable functions. Math. Proc. Camb. Phil. Soc. 140, no. 2, 269-295 (2006)
  14. (with K. Kawamura) On the coordinate functions of Lévy's dragon curve. Real Anal. Exchange 31, no. 1, 295-308 (2005/06)
  15. Prophet regions for discounted, uniformly bounded random variables. Stoch. Anal. Appl. 24, no. 3, 531-554 (2006)
  16. Prophet inequalities for i.i.d. random variables with random arrival times. Sequential Anal. 26, no. 4, 403-413 (2007)
  17. (with K. Kawamura) Dimensions of the coordinate functions of space-filling curves. J. Math. Anal. Appl. 335, 1161-1176 (2007)
  18. (with M. Monticino) Optimal buy/sell strategies for directionally reinforced processes. J. Appl. Prob. 45, 33-44 (2008)
  19. Distribution of the maxima of random Takagi functions. Acta Math. Hungarica  121, no. 3, 243-275 (2008)
  20. On a flexible class of continuous functions with uniform local structure. J. Math. Soc. Japan  61, no. 1, 237-262 (2009)
  21. (with R. D. Mauldin) Injectivity of the Dubins-Freedman construction of random distributions. Contemp. Math. 485, 1-11 (2009)
  22. A sharp ratio inequality for optimal stopping when only relative record times are observed. Sequential Anal. 28, no. 4, 455-458 (2009)
  23. Optimal stopping rules for American and Russian options in a correlated random walk modelStoch. Models 26, no. 4, 594-616 (2010)
  24. 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
  25. Predicting the supremum: optimality of "stop at once or not at all" (To appear in J. Appl. Probab. (2012); arXiv:0912.0615)
  26. (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
  27. 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
  28. The finite cardinalities of level sets of the Takagi function. J. Math. Anal. Appl. 388 (2012), no. 2, 1117–1129;  arXiv:1107.0712
  29. How large are the level sets of the Takagi function? Monatsh. Math. 167 (2012), 311-331;  arXiv:1102.1616
  30. (with K. Kawamura) The Takagi function: a survey. Real Anal. Exchange 37 (2011/12), no. 1, 1-54;  arXiv:1110.1691
  31. Level sets of signed Takagi functions.  Acta Math. Hungarica 141 (2013), no. 4, 339-352;   arXiv:1209.6120
  32. Digital sum inequalities and approximate convexity of Takagi-type functions. Math. Ineq. Appl. 17 (2014), no. 2, 679-691;  arXiv:1208.2745
  33. On the level sets of the Takagi-van der Waerden functions. J. Math. Anal. Appl. 419, (2014), 1168-1180;  arXiv:1312.2119
  34. 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
  35. Hausdorff dimension of level sets of generalized Takagi functions. Math. Proc. Camb. Phil. Soc. 157 (2014), 253-278;  arXiv:1301.4747
  36. The infinite derivatives of Okamoto's function: an application of beta-expansions. J. Fractal Geom. 3 (2016), no. 1, 1-31;  arXiv:1502.03374
  37. (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
  38. On univoque and strongly univoque sets.  Adv. Math. 308 (2017), 575-598;  arXiv:1601.04680v2
  39. Differentiability of a two-parameter family of self-affine functions.  J. Math. Anal. Appl. 450 (2017), no. 2, 954–968;  arXiv:1606.07838
  40. Differentiability and Holder spectra of a class of self-affine functions.  Adv. Math. 328 (2018), 1--39;  arXiv:1707.07376v2
  41. (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
  42. (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
  43. 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
  44. (with A. Allen) A random walk version of Robbins' problem: small horizon.  Math. Appl. 47 (2019), no. 2, 293-312; link to arXiv
  45. 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
  46. (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
  47. (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
  48. (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
  49. (with D. Kong) Density spectrum of Cantor measure. Submitted for publication, 27 pages (2021); link to arXiv
  50. (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)
  51. (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
  52. (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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