{"paper":{"title":"Numerical solution of fractional elliptic stochastic PDEs with spatial white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.CO"],"primary_cat":"math.NA","authors_text":"David Bolin, Kristin Kirchner, Mih\\'aly Kov\\'acs","submitted_at":"2017-05-18T13:06:44Z","abstract_excerpt":"The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in $\\mathbb{R}^d$ is considered. The differential operator is given by the fractional power $L^\\beta$, $\\beta\\in(0,1)$, of an integer order elliptic differential operator $L$ and is therefore non-local. Its inverse $L^{-\\beta}$ is represented by a Bochner integral from the Dunford-Taylor functional calculus. By applying a quadrature formula to this integral representation, the inverse fractional power operator $L^{-\\beta}$ is approximated by a weighted sum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06565","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1705.06565/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"}