17 citations · 59 across the 22 of their papers we have counts for
6 papers · 1 filter
Random subsets of Cantor sets generated by trees of coin flips
Pieter Allaart, Taylor Jones
We introduce a natural way to construct a random subset of a homogeneous Cantor set in via random labelings of an infinite -ary tree, where . The Cantor set…
A random walk version of Robbins' problem: small horizon
Pieter C. Allaart, Andrew Allen
In Robbins' problem of minimizing the expected rank, a finite sequence of independent, identically distributed random variables are observed sequentially and the objective is t…
A sharp lower bound for choosing the maximum of an independent sequence
Pieter C. Allaart, Jose A. Islas
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The…
Predicting the supremum: optimality of "stop at once or not at all"
Pieter C. Allaart
Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t "as close as possi…
A general "bang-bang" principle for predicting the maximum of a random walk
Pieter C. Allaart
Let be either a Bernoulli random walk or a Brownian motion with drift, and let , . This paper solves the gen…
Prophet inequalities for i.i.d. random variables with random arrival times
Pieter C. Allaart
Suppose are i.i.d. nonnegative random variables with finite expectation, and for each , is observed at the -th arrival time of a Poisson process wit…