{"paper":{"title":"Refined basic couplings and Wasserstein-type distances for SDEs with L\\'{e}vy noises","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dejun Luo, Jian Wang","submitted_at":"2016-04-25T11:25:27Z","abstract_excerpt":"We establish the exponential convergence with respect to the $L^1$-Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation (SDE)\n  $$d X_t=d Z_t+b(X_t)\\,d t,$$ where $(Z_t)_{t\\ge0}$ is a pure jump L\\'{e}vy process whose L\\'{e}vy measure $\\nu$ fulfills\n  $$ \\inf_{x\\in \\R^d, |x|\\le \\kappa_0} [\\nu\\wedge (\\delta_x \\ast \\nu)]( \\R^d)>0$$ for some constant $\\kappa_0>0$, and the drift term $b$ satisfies that for any $x,y\\in \\R^d$,\n  $$\\langle b(x)-b(y),x-y\\rangle\\le \\begin{cases}\n  \\Phi_1(|x-y|)|x-y|,& |x-y|\\le l_0;\n  -K_2|x-y|^2,& |x-y|> l_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07206","kind":"arxiv","version":2},"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"}