Exponential convergence in ‐Wasserstein distance for diffusion processes without uniformly dissipative drift |
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| Authors: | Dejun Luo Jian Wang |
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| Affiliation: | 1. +86 2. 10 3. 8254 4. 1312+86 5. 1972;6. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;7. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, China |
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| Abstract: | By adopting the coupling by reflection and choosing an auxiliary function which is convex near infinity, we establish the exponential convergence of diffusion semigroups  with respect to the standard  ‐Wasserstein distance for all  . In particular, we show that for the Itô stochastic differential equation ![urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0006]( "urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0006") if the drift term b is such that for any  , ![urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0008]( "urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0008") holds with some positive constants K1, K2 and  , then there is a constant  such that for all  ,  and  , ![urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0014]( "urn:x-wiley:0025584X:media:mana201500351:mana201500351-math-0014") where  is a positive constant. This improves the main result in 14 where the exponential convergence is only proved for the L1‐Wasserstein distance. |
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| Keywords: | Exponential convergence ‐Wasserstein distance coupling by reflection diffusion process 60H10 |
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