{"paper":{"title":"Stochastic flows for L\\'evy processes with H\\\"{o}lder drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Renming Song, Xicheng Zhang, Zhen-Qing Chen","submitted_at":"2015-01-20T10:42:33Z","abstract_excerpt":"In this paper we study the following stochastic differential equation (SDE) in ${\\mathbb R}^d$: $$ \\mathrm{d} X_t= \\mathrm{d} Z_t + b(t, X_t)\\mathrm{d} t, \\quad X_0=x, $$ where $Z$ is a L\\'evy process. We show that for a large class of L\\'evy processes ${Z}$ and H\\\"older continuous drift $b$, the SDE above has a unique strong solution for every starting point $x\\in{\\mathbb R}^d$. Moreover, these strong solutions form a $C^1$-stochastic flow. As a consequence, we show that, when ${Z}$ is an $\\alpha$-stable-type L\\'evy process with $\\alpha\\in (0, 2)$ and $b$ is bounded and $\\beta$-H\\\"older conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04758","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"}