16 citations · 31 across the 6 of their papers we have counts for
7 papers · 1 filter
A central limit theorem for costs in Bulinskaya's inventory management problem when deliveries face delays
Alessandro Arlotto, J. Michael Steele
It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variab…
The Bruss-Robertson Inequality: Elaborations, Extensions, and Applications
J. Michael Steele
The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality whi…
Quickest Online Selection of an Increasing Subsequence of Specified Size
Alessandro Arlotto, Elchanan Mossel, J. Michael Steele
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of th…
Optimal Online Selection of a Monotone Subsequence: a Central Limit Theorem
Alessandro Arlotto, Vinh V. Nguyen, J. Michael Steele
Consider a sequence of independent random variables with a common continuous distribution , and consider the task of choosing an increasing subsequence where the observation…
Beardwood-Halton-Hammersley Theorem for Stationary Ergodic Sequences: a Counterexample
Alessandro Arlotto, J. Michael Steele
We construct a stationary ergodic process such that each has the uniform distribution on the unit square and the length of the shortest path through…
A Systematic Martingale Construction with Applications to Permutation Inequalities
Vladimir Pozdnyakov, J. Michael Steele
We illustrate a process that constructs martingales from raw material that arises naturally from the theory of sampling without replacement.The usefulness of the new martingales is…