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 model. Stoch. 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

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