{"paper":{"title":"Occupation times of refracted L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas E. Kyprianou, J.C. Pardo, J.L. P\\'erez","submitted_at":"2012-05-03T16:27:19Z","abstract_excerpt":"A refracted L\\'evy process is a L\\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted L\\'evy process is described by the unique strong solution to the stochastic differential equation \\[ \\ud U_t=-\\delta\\mathbf{1}_{\\{U_t>b\\}}\\ud t +\\ud X_t, \\] where $X=(X_t, t\\ge 0)$ is a L\\'evy process with law $\\p$ and $b,\\delta\\in \\R$ such that the resulting process $U$ may visit the half line $(b,\\infty)$ with positive probability. In this paper, we conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0756","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"}