{"paper":{"title":"Randomised Euler-Maruyama Method for SDEs with H\\\"older Continuous Drift Coefficient Driven by $\\alpha$-stable L\\'evy Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danqi Zhuang, Haitao Wang, Jianhai Bao, Yue Wu","submitted_at":"2025-07-15T15:52:55Z","abstract_excerpt":"In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift driven by symmetric $\\alpha$-table process, $\\alpha\\in (1,2)$. In particular, the drift is assumed to be $\\beta$-H\\\"older continuous in time and bounded $\\eta$-H\\\"older continuous in space with $\\beta,\\eta\\in (0,1]$. The strong order of convergence of the randomised EM in $L^p$-norm is shown to be $1/2+(\\beta \\wedge (\\eta/\\alpha)\\wedge(1/2))-\\varepsilon$ for an arbitrary $\\varepsilon\\in (0,1/2)$, higher than the one of standard EM, which cannot exceed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11429","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/2507.11429/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"}