{"paper":{"title":"Uniqueness for the Skorokhod problem in an orthant: critical cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy, Richard F. Bass","submitted_at":"2024-07-06T17:38:19Z","abstract_excerpt":"Consider the Skorokhod problem in the closed non-negative orthant: find a solution $(g(t),m(t))$ to \\[ g(t)= f(t)+ Rm(t),\\] where $f$ is a given continuous vector-valued function with $f(0)$ in the orthant, $R$ is a given $d\\times d$ matrix with 1's along the diagonal, $g$ takes values in the orthant, and $m$ is a vector-valued function that starts at 0, each component of $m$ is non-decreasing and continuous, and for each $i$ the $i^{th}$ coordinate of $m$ increases only when the $i^{th}$ coordinate of $g$ is 0. The stochastic version of the Skorokhod problem replaces $f$ by the paths of Brown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05140","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.05140/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}