{"paper":{"title":"Exponential Convergence in $L^p$-Wasserstein Distance for Diffusion Processes without Uniformly Dissipative Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dejun Luo, Jian Wang","submitted_at":"2014-07-08T08:18:35Z","abstract_excerpt":"By adopting the coupling by reflection and choosing an auxiliary function which is convex near infinity, we establish the exponential convergence of diffusion semigroups $(P_t)_{t\\ge0}$ with respect to the standard $L^p$-Wasserstein distance for all $p\\in[1,\\infty)$. In particular, we show that for the It\\^o stochastic differential equation\n  $$\\d X_t=\\d B_t+b(X_t)\\,\\d t,$$ if the drift term $b$ satisfies that for any $x,y\\in\\R^d$,\n  $$\\langle b(x)-b(y),x-y\\rangle\\le \\begin{cases}\n  K_1|x-y|^2,& |x-y|\\le L;\n  -K_2|x-y|^2,& |x-y|> L\n  \\end{cases}$$ holds with some positive constants $K_1$, $K_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1986","kind":"arxiv","version":3},"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"}