{"paper":{"title":"Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Levy noise","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Konstantinos Dareiotis, M\\'at\\'e Gerencs\\'er, Oleg Butkovsky","submitted_at":"2022-04-27T13:28:35Z","abstract_excerpt":"We study the strong rate of convergence of the Euler--Maruyama scheme for a multidimensional stochastic differential equation (SDE) $$ dX_t = b(X_t) \\, dt + dL_t, $$ with irregular $\\beta$-H\\\"older drift, $\\beta > 0$, driven by a L\\'evy process with exponent $\\alpha \\in (0, 2]$. For $\\alpha \\in [2/3, 2]$, we obtain strong $L_p$ and almost sure convergence rates in the entire range $\\beta > 1 - \\alpha/2$, where the SDE is known to be strongly well-posed. This significantly improves the current state of the art, both in terms of convergence rate and the range of $\\alpha$. Notably, the obtained c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12926","kind":"arxiv","version":2},"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/2204.12926/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"}