2025/11/26 by A. M. Kabaeva, Kabaeva, A. M., A. V. Logachov +3
Computer Science · Decision Sciences · #Advanced Statistical Process Monitoring #FOS: Mathematics #Optimization and Search Problems #Probability (math.PR) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2511.21370
openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28
Bruss's odds theorem \citeBruss1 addresses the problem of determining the optimal stopping time for sequences of independent indicator functions. In this note, we derive upper and lower bounds for the success probability under the optimal stopping rule. These bounds depend on the number of independent events under consideration and on a deterministic index specifying the stopping time. Moreover, the bounds are sharp: we provide explicit examples in which the corresponding inequalities are attained with equality.