{"paper":{"title":"Volterra differential equations with singular kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laure Coutin (LSProba), Laurent Decreusefond","submitted_at":"2017-03-24T12:56:29Z","abstract_excerpt":"Motivated by the potential applications to the fractional Brownianmotion, we study Volterra stochasticdifferential of the form~:\\begin{equation}X\\_t =  x+ \\int\\_0^tK(t,s)b(s,X\\_s)ds + \\int\\_0^tK(t,s) \\sigma(s,X\\_s)\\,dB\\_s ,\\tag{E} \\label{eq:sdefbm}\\end{equation}where $(B\\_s, \\, s\\in [0,1])$ is a one-dimensional standard Brownianmotion and $(K(t,s), \\, t,s \\in [0,1])$ is a deterministic kernelwhose properties will be precised below but for which we don't assumeany boundedness property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08395","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"}