The dimension-free Harnack inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in Feng and Wang (J. Appl. Probab. 44 938–949 2007) to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev inequality which strengthens the log-Sobolev inequality derived in Feng and Wang (J. Appl. Probab. 44 938–949 2007). To prove the main results, explicit Harnack inequality and super Poincaré inequality are established for the one-dimensional Wright-Fisher diffusion processes. The main tool of the study is the coupling by change of measures.
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Supported in part by NNSFC(11131003, 11431014), the 985 project, the Laboratory of Mathematical and Complex Systems, and NSERC.
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Feng, S., Wang, FY. Harnack Inequality and Applications for Infinite-Dimensional GEM Processes. Potential Anal 44, 137–153 (2016). https://doi.org/10.1007/s11118-015-9502-5
- GEM distribution
- GEM diffusion process
- Harnack inequality
- Heat kernel
- Super log-Sobolev inequality
Mathematics Subject Classification (2010)