{"paper":{"title":"The nonlinear Schr\\\"odinger Equation driven by jump processes","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anne de Bouard, Erika Hausenblas","submitted_at":"2017-02-08T17:04:45Z","abstract_excerpt":"The main result of the paper is the existence of a solution of the nonlinear Schr\\\"odinger equation with a \\levy noise with infinite activity. To be more precise, let $A=\\Delta$ be the Laplace operator with $D(A)=\\{ u\\in L ^2 (\\mathbb{R} ^d): \\Delta u \\in L ^2 (\\mathbb{R} ^d)\\}$. Let $Z\\hookrightarrow L ^2(\\mathbb{R} ^d)$ be a function space and $\\eta$ be a Poisson random measure on $Z$, let $g:\\mathbb{R}\\to\\mathbb{C}$ and $h:\\mathbb{R}\\to\\mathbb{C}$ be some given functions, satisfying certain conditions specified later. Let $\\alpha\\ge 1$ and $\\lambda\\ge 0$. We are interested in the solution o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02523","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"}