Optimal Stopping for the Uniform Distribution

Alexander Gnedin

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arXiv · 2601.04371

Optimal Stopping for the Uniform Distribution

Alexander Gnedin

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Abstract

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.

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Alexander Gnedin. 2026-01-07. Optimal Stopping for the Uniform Distribution. https://arxiv.org/abs/2601.04371

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