{"paper":{"title":"Prophet inequalities for i.i.d. random variables with random arrival times","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pieter C. Allaart","submitted_at":"2006-11-21T22:59:47Z","abstract_excerpt":"Suppose $X_1,X_2,...$ are i.i.d. nonnegative random variables with finite expectation, and for each $k$, $X_k$ is observed at the $k$-th arrival time $S_k$ of a Poisson process with unit rate which is independent of the sequence $\\{X_k\\}$. For $t>0$, comparisons are made between the expected maximum $M(t):=\\rE[\\max_{k\\geq 1} X_k \\sI(S_k\\leq t)]$ and the optimal stopping value $V(t):=\\sup_{\\tau\\in\\TT}\\sE[X_\\tau \\sI(S_\\tau\\leq t)]$, where $\\TT$ is the set of all $\\NN$-valued random variables $\\tau$ such that $\\{\\tau=i\\}$ is measurable with respect to the $\\sigma$-algebra generated by $(X_1,S_1),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611664","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}