{"paper":{"title":"SPDEs with two reflecting walls and two singular drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianliang Zhai, Juan Yang","submitted_at":"2015-05-15T01:50:22Z","abstract_excerpt":"We study SPDEs with two reflecting walls $\\Lambda^1$, $\\Lambda^2$ and two singular drifts $\\frac{c_1}{(X-\\Lambda^1)^{\\vartheta}}$, $\\frac{c_2}{(\\Lambda^2-X)^{\\vartheta}}$, driven by space-time white noise. First, we establish the existence and uniqueness of the solutions $X$ for $\\vartheta\\geq 0$. Second, we obtain the following pathwise properties of the solutions $X$. If $\\vartheta>3$, then a.s. $\\Lambda^1<X<\\Lambda^2$ for all $t\\geq0$; If $0<\\vartheta<3$, then $X$ hits $\\Lambda^1$ or $\\Lambda^2$ with positive probability in finite time. Thus $\\vartheta=3$ is the critical parameter for $X$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03938","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"}