THE INFINITE SECRETARY PROBLEM WITH RECALL
成果类型：
Article
署名作者：
ROCHA, AL
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989273
发表日期：
1993
页码：
898-916
关键词：
摘要：
The infinite secretary problem, in which an infinite number of rankable items arrive at times which are i.i.d., uniform on (0, 1), is modified to allow for a fixed period of recall of length alpha, 0 less-than-or-equal-to alpha less-than-or-equal-to 1. The goal is to find the maximum probability of best choice, v = v(alpha), as well as an optimal stopping time tau* = tau*(alpha). A differential-delay equation is derived, the solution of which yields v(alpha) and tau*(a), the latter given in terms of a constant t* [= t*(alpha)]. For alpha greater-than-or-equal-to 1/2, the complete solution to the problem is obtained. For 0 < a < 1/2, nu(alpha) cannot be put in closed form, so upper and lower bounds for v(alpha) and t*(a) are obtained and are investigated for alpha near 0 and near 1/2, where the solutions are known. We also find asymptotic expansions of v(alpha) and t*(alpha) about alpha = 0 and alpha = 1/2. Finally, the solution to the finite, n-item length-m recall problem introduced by Smith and Deely is shown to converge to the solution of the infinite problem when m/n --> alpha.