{"paper":{"title":"Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Buyang Li, Jilu Wang, Max Gunzburger","submitted_at":"2017-04-10T15:37:21Z","abstract_excerpt":"The stochastic time-fractional equation $\\partial_t \\psi -\\Delta\\partial_t^{1-\\alpha} \\psi = f + \\dot W$ with space-time white noise $\\dot W$ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate \\[ {\\mathbb E}\\|\\psi(\\cdot,t_n)-\\psi_n\\|_{L^2(\\mathcal{O})}^2=O(\\tau^{1-\\alpha d/2}) \\] is established for $\\alpha\\in(0,2/d)$, where $d$ denotes the spatial dimension, $\\psi_n$ the approximate solution at the $n^{\\rm th}$ time step, and $\\mathbb{E}$ the expectation operator. In particular, the result indicates optimal convergence rates of numerical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02912","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"}