{"paper":{"title":"A note on stochastic Schr\\\"odinger equations with fractional multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Olivier Pinaud","submitted_at":"2013-03-29T17:14:10Z","abstract_excerpt":"This work is devoted to non-linear stochastic Schr\\\"odinger equations with multiplicative fractional noise, where the stochastic integral is defined following the Riemann-Stieljes approach of Z\\\"ahle. Under the assumptions that the initial condition is in the Sobolev space $H^q(\\Rm^n)$ for a dimension $n$ less than three and $q$ an integer greater or equal to zero, that the noise is a $Q-$fractional Brownian motion with Hurst index $H\\in(1/2,1)$ and spatial regularity $H^{q+4}(\\Rm^n)$, as well as appropriate hypotheses on the non-linearity, we obtain the local existence of a unique pathwise so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7442","kind":"arxiv","version":1},"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"}