Best Choice from the Planar Poisson Process
Probability
2007-05-23 v2
Abstract
Various best-choice problems related to the planar homogeneous Poisson process in finite or semi-infinite rectangle are studied. The analysis is largely based on properties of the one-dimensional box-area process associated with the sequence of records. We prove a series of distributional identities involving exponential and uniform random variables, and resolve the Petruccelli-Porosinski-Samuels paradox on coincidence of asymptotic values in certain discrete-time optimal stopping problems.
Cite
@article{arxiv.math/0209050,
title = {Best Choice from the Planar Poisson Process},
author = {Alexander Gnedin},
journal= {arXiv preprint arXiv:math/0209050},
year = {2007}
}
Comments
35 pages