{"paper":{"title":"An explicit formula for the Skorokhod map on $[0,a]$","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"John Lehoczky, Kavita Ramanan, Lukasz Kruk, Steven Shreve","submitted_at":"2007-10-16T08:22:52Z","abstract_excerpt":"The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map $\\Gamma_{0,a}$ on $[0,a]$ for any $a>0$ is derived. Specifically, it is shown that on the space $\\mathcal{D}[0,\\infty)$ of right-continuous functions with left limits taking values in $\\mathbb{R}$, $\\Gamma_{0,a}=\\Lambda_a\\circ \\Gamma_0$, where $\\Lambda_a:\\mathcal{D}[0,\\infty)\\to\\mathcal{D}[0,\\infty)$ is defined by \\[\\Lambda_a(\\phi)(t)=\\phi(t)-\\sup_{s\\in[0,t]}\\biggl[\\bigl(\\ phi(s)-a\\bigr)^+\\wedge\\inf_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2977","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"}