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Nash inequality for diffusion processes associated with Dirichlet distributions |
Feng-Yu WANG1,2(), Weiwei ZHANG3 |
1. Center for Applied Mathematics, Tianjin University, Tianjin 300072, China 2. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK 3. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
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Abstract For any and , let be the Dirichlet distribution with parameter α on the set . The multivariate Dirichlet diffusion is associated with the Dirichlet form
with Domain being the closure of . We prove the Nash inequality
for some constant and , where the constant p is sharp when and . This Nash inequality also holds for the corresponding Fleming-Viot process.
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Keywords
Dirichlet distribution
Nash inequality
super Poincaré inequality
diffusion process
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Corresponding Author(s):
Feng-Yu WANG
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Issue Date: 07 January 2020
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