Optimal Stopping for the Uniform Distribution
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914239615074304 |
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| author | Gnedin, Alexander |
| author_facet | Gnedin, Alexander |
| contents | Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform random variables, in the asymptotic regime where $n$ and the range of distribution are of the same order. The optimal stopping rule in the Poisson problem is identified, by means of a time change, with known asymptotic solution to Lindley's problem of minimising the expected rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Stopping for the Uniform Distribution Gnedin, Alexander Probability 60G40 Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform random variables, in the asymptotic regime where $n$ and the range of distribution are of the same order. The optimal stopping rule in the Poisson problem is identified, by means of a time change, with known asymptotic solution to Lindley's problem of minimising the expected rank. |
| title | Optimal Stopping for the Uniform Distribution |
| topic | Probability 60G40 |
| url | https://arxiv.org/abs/2601.04371 |