{"paper":{"title":"Approximation of stochastic processes by non-expansive flows and coming down from infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Vincent Bansaye (CMAP)","submitted_at":"2015-11-23T20:18:56Z","abstract_excerpt":"We approximate stochastic processes in finite dimension  by dynamical systems.  We provide trajectorial  estimates which are uniform with respect to the initial condition for a well chosen distance.  This relies on some non-expansivity property of the  flow, which allows to deal with  non-Lipschitz vector fields. We use the  stochastic calculus  and   follow  the martingale technics  initiated in Berestycki and al [5] to control the fluctuations. Our main applications deal with the short time behavior  of   stochastic processes starting from large initial values.  We  state  general properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07396","kind":"arxiv","version":4},"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"}