2002/09/05 by Alexander Gnedin, Gnedin, Alexander
Mathematics · #60G40 #60G70 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G40 #msc:60G70
paper · pdf · doi:10.48550/arxiv.math/0209050
35 pages
arxiv created 2002/09/09 · arxiv updated 2009/11/30
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.