{"paper":{"title":"An Osgood's criterion for a semilinear stochastic differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jorge A. Le\\'on, Jos\\'e Villa-Morales, Liliana Peralta","submitted_at":"2014-01-30T16:19:06Z","abstract_excerpt":"The purpose of this paper is to give an Osgood's criterion for solutions of semilinear stochastic differential equations of the form $X_{t}=\\xi +\\int_{0}^{t}b(s,X_{s})ds+\\int_{0}^{t}\\sigma (s)X_{s}dW_{s},\\ t\\geq 0$. Here, $b$ is a non-negative, non-decreasing by components and continuous random field and $\\sigma $ is a predictable and continuous process. Also we present a generalization of the so-called Feller's test whenever $\\sigma \\equiv 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7905","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"}