{"paper":{"title":"SPDEs with fractional noise in space with index $H<1/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lluis Quer-Sardanyons, Maria Jolis, Raluca Balan","submitted_at":"2014-07-15T18:13:36Z","abstract_excerpt":"In this article, we consider the stochastic wave and heat equations on $\\mathbb{R}$ with non-vanishing initial conditions, driven by a Gaussian noise which is white in time and behaves in space like a fractional Brownian motion of index $H$, with $1/4<H<1/2$. We assume that the diffusion coefficient is given by an affine function $\\sigma(x)=ax+b$, and the initial value functions are bounded and H\\\"older continuous of order $H$. We prove the existence and uniqueness of the mild solution for both equations. We show that the solution is $L^{2}(\\Omega)$-continuous and its $p$-th moments are unifor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4080","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"}