{"paper":{"title":"Pathwise uniqueness for a SPDE with H\\\"older continuous coefficient driven by \\alpha-stable noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiaowen Zhou, Xu Yang","submitted_at":"2013-05-24T05:43:04Z","abstract_excerpt":"In this paper we study the pathwise uniqueness of solution to the following stochastic partial differential equation (SPDE) with H\\\"older continuous coefficient:\n  \\begin{eqnarray*} \\frac{\\partial X_t(x)}{\\partial t}=\\frac{1}{2} \\Delta X_t(x) +G(X_t(x))+H(X_{t-}(x)) \\dot{L}_t(x),~~~ t>0, ~x\\in\\mathbb{R},\n  \\end{eqnarray*} where $\\dot{L}$ denotes an $\\alpha$-stable white noise on $\\mathbb{R}_+\\times \\mathbb{R}$ without negative jumps, $G$ satisfies the Lipschitz condition and $H$ is nondecreasing and $\\beta$-H\\\"older continuous for $1<\\alpha<2$ and $0<\\beta<1$.\n  For $G\\equiv0$ and $H(x)=x^\\bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5624","kind":"arxiv","version":3},"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"}