{"paper":{"title":"Approximation of the invariant measure for stable SDE by the Euler-Maruyama scheme with decreasing step-sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA"],"primary_cat":"math.PR","authors_text":"Lihu Xu, Peng Chen, Xinghu Jin, Yimin Xiao","submitted_at":"2023-10-09T03:59:14Z","abstract_excerpt":"Let $(X_t)_{t \\ge 0}$ be the solution of the stochastic differential equation $$dX_t = b(X_t) dt+A dZ_t, \\quad X_{0}=x,$$ where $b: \\mathbb{R}^d \\rightarrow \\mathbb R^d$ is a Lipschitz function, $A \\in \\mathbb R^{d \\times d}$ is a positive definite matrix, $(Z_t)_{t\\geq 0}$ is a $d$-dimensional rotationally invariant $\\alpha$-stable L\\'evy process with $\\alpha \\in (1,2)$ and $x\\in\\mathbb{R}^{d}$. We use two Euler-Maruyama schemes with decreasing step sizes $\\Gamma = (\\gamma_n)_{n\\in \\mathbb{N}}$ to approximate the invariant measure of $(X_t)_{t \\ge 0}$: one with i.i.d. $\\alpha$-stable distribu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05390","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/2310.05390/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"}