{"paper":{"title":"$L^p$-Wasserstein distance for stochastic differential equations driven by L\\'{e}vy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jian Wang","submitted_at":"2016-03-17T13:50:39Z","abstract_excerpt":"Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by L\\'{e}vy noises. As an application, we establish the exponential contractivity of the associated semigroups $(P_t)_{t\\ge0}$ with respect to the standard $L^p$-Wasserstein distance for all $p\\in[1,\\infty)$. In particular, consider the following SDE: \\[\\mathrm{d}X_t=\\mathrm{d}Z_t+b(X_t)\\,\\mathrm{d}t,\\] where $(Z_t)_{t\\ge0}$ is a symmetric $\\alpha$-stable process on $\\mathbb{R}^d$ with $\\alpha\\in(1,2)$. We show that if the drift term $b$ satisfies that for any $x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05484","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"}