Harnack Inequality and Applications for Infinite-Dimensional GEM Processes

Shui Feng; Feng-Yu Wang

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arXiv · 1410.3936

Harnack Inequality and Applications for Infinite-Dimensional GEM Processes

Shui Feng·Feng-Yu Wang

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Abstract

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 \cite{FW} 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 \cite{FW}. To prove the main results, explicit Harnack inequality and super Poincar\'e 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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BibTeX RIS

Shui Feng, Feng-Yu Wang. 2014-10-15. Harnack Inequality and Applications for Infinite-Dimensional GEM Processes. https://arxiv.org/abs/1410.3936

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