{"paper":{"title":"Existence of strong solutions for It\\^o's stochastic equations via approximations. Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"I. Gy\\\"ongy, N.V. Krylov","submitted_at":"2021-07-30T01:18:58Z","abstract_excerpt":"Given strong uniqueness for an It\\^o's stochastic equation, we prove that its solution can beconstructed on \"any\" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\\mathbb{R}^{d}$ and in domains in $\\mathbb{R}^{d}$ are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of \"tamed Euler approximations\" for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.14384/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}