A New Probability Measure-Valued Stochastic Process with Ferguson-Dirichlet Process as Reversible Measure

Jinghai Shao (Beijing Normal University)

Abstract


A new diffusion process taking values in the space of all probability measures over $[0,1]$ is constructed through Dirichlet form theory in this paper. This process is reversible with respect to the Ferguson-Dirichlet process (also called Poisson Dirichlet process), which is the reversible measure of the Fleming-Viot process with parent independent mutation. The intrinsic distance of this process is in the class of Wasserstein distances, so it's also a kind of Wasserstein diffusion. Moreover, this process satisfies the Log-Sobolev inequality.

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Pages: 271-292

Publication Date: January 26, 2011

DOI: 10.1214/EJP.v16-844

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