# A note on a lower bound for the multiplicative odds theorem of optimal stopping

Tomomi Matsui, Katsunori Ano

3 被引用数 (Scopus)

## 抄録

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 < m < N. This problem is an extension of Bruss' (2000) odds problem. In a previouswork, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem..

本文言語 English 885-889 5 Journal of Applied Probability 51 3 https://doi.org/10.1239/jap/1409932681 Published - 2014 9月 1

## ASJC Scopus subject areas

• 統計学および確率
• 数学 (全般)
• 統計学、確率および不確実性

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