{"paper":{"title":"$W_{\\bf d}$-convergence rate of EM schemes for invariant measures of supercritical stable SDEs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Peng Chen, XiaoLong Zhang, Xicheng Zhang","submitted_at":"2024-11-15T05:02:50Z","abstract_excerpt":"By establishing the regularity estimates for nonlocal Stein/Poisson equations under $\\gamma$-order H\\\"older and dissipative conditions on the coefficients, we derive the $W_{\\bf d}$-convergence rate for the Euler-Maruyama schemes applied to the invariant measure of SDEs driven by multiplicative $\\alpha$-stable noises with $\\alpha \\in (\\frac{1}{2}, 2)$, where $W_{\\bf d}$ denotes the Wasserstein metric with ${\\bf d}(x,y)=|x-y|^\\gamma\\wedge 1$ and $\\gamma \\in ((1-\\alpha)_+, 1]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09949","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/2411.09949/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"}