This article considers an analogous problem in which the observed random variables are the steps of a symmetric random walk. Assuming continuously distributed step sizes, it describes the optimal stopping rules for the cases n = 2 and n = 3 in two versions of the problem: a "full information" version in which the actual steps of the random walk are disclosed to the decision maker; and a "partial information" version in which only the relative ranks of the positions taken by the random walk are observed. When n = 3, the optimal rule and expected rank depend on the distribution of the step sizes. The authors give sharp bounds for the optimal expected rank in the partial information version, and fairly sharp bounds in the full information version.

Video from the Fall 2018 3 Minute Thesis (3MT®) Final Competition. In this video, Muthappan Asokan presents his research methods, findings, and its significance in non-technical language.

Video from the Fall 2018 3 Minute Thesis (3MT®) Final Competition. In this video, Devasantosh Mohanty presents his research methods, findings, and its significance in non-technical language.

Video from the Fall 2018 3 Minute Thesis (3MT®) Final Competition. In this video, Sujata Argawal presents her research methods, findings, and its significance in non-technical language.