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• W3004736679 abstract "Let Pt be the (Neumann) diffusion semigroup Pt generated by a weighted Laplacian on a complete connected Riemannian manifold M without boundary or with a convex boundary. It is well known that the Bakry-Emery curvature is bounded below by a positive constant ≪> 0 if and only if $$W_{p}(mu_{1}P_{t}, mu_{2}P_{t})leq e^{-ll t} W_{p} (mu_{1},mu_{2}), tgeq 0, pgeq 1 $$ holds for all probability measures μ1 and μ2 on M, where Wp is the Lp Wasserstein distance induced by the Riemannian distance. In this paper, we prove the exponential contraction $$W_{p}(mu_{1}P_{t}, mu_{2}P_{t})leq ce^{-ll t} W_{p} (mu_{1},mu_{2}), p geq 1, tgeq 0$$ for some constants c,≪> 0 for a class of diffusion semigroups with negative curvature where the constant c is essentially larger than 1. Similar results are derived for SDEs with multiplicative noise by using explicit conditions on the coefficients, which are new even for SDEs with additive noise." @default.
• W3004736679 created "2020-02-14" @default.
• W3004736679 creator A5043138062 @default.
• W3004736679 date "2020-02-06" @default.
• W3004736679 modified "2023-10-09" @default.
• W3004736679 title "Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature" @default.
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• W3004736679 doi "https://doi.org/10.1007/s11118-019-09800-z" @default.
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