{"paper":{"title":"Convergence of a $\\theta$-scheme to solve the stochastic nonlinear Schr\\\"odinger equation with Stratonovich noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andreas Prohl, Chuchu Chen, Jialin Hong","submitted_at":"2014-10-23T03:12:28Z","abstract_excerpt":"We propose a $\\theta$-scheme to discretize the $d$-dimensional stochastic cubic Schr\\\"odinger equation in Stratono\\-vich sense. A uniform bound for the Hamiltonian of the discrete problem is obtained, which is a crucial property to verify the convergence in probability towards a mild solution.\n  Furthermore, based on the uniform bounds of iterates in ${\\mathbb H}^2(\\mathcal{O})$ for $\\mathcal{O}\\subset\\mathbb{R}^{1}$, the optimal convergence order 1 in strong local sense is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6231","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"}