Harnack Inequality and Applications for Infinite-Dimensional GEM Processes
Probability
2014-10-16 v1
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.
Cite
@article{arxiv.1410.3936,
title = {Harnack Inequality and Applications for Infinite-Dimensional GEM Processes},
author = {Shui Feng and Feng-Yu Wang},
journal= {arXiv preprint arXiv:1410.3936},
year = {2014}
}
Comments
19 pages