{"paper":{"title":"Strong rate of convergence for the Euler-Maruyama approximation of SDEs with H\\\"older continuous drift coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dai Taguchi, Olivier Menoukeu Pamen","submitted_at":"2015-08-29T23:47:22Z","abstract_excerpt":"In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \\int_{0}^{t} b(s, X_{s}) \\mathrm{d}s + L_{t},~x_{0} \\in \\mathbb{R}^{d},~t \\in [0,T],$$ where the drift coefficient $b:[0,T] \\times \\mathbb{R}^d \\to \\mathbb{R}^d$ is H\\\"older continuous in both time and space variables and the noise $L=(L_t)_{0 \\leq t \\leq T}$ is a $d$-dimensional L\\'evy process. We provide the rate of convergence for the Euler-Maruyama approximation when $L$ is a Wiener process or a truncated symmetric $\\alpha$-stable process with $\\alpha \\in (1,2)$. Our technique "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07513","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":""},"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"}