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


 
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1. Title Title of document A New Probability Measure-Valued Stochastic Process with Ferguson-Dirichlet Process as Reversible Measure
 
2. Creator Author's name, affiliation, country Jinghai Shao; Beijing Normal University; China
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Wasserstein diffusion; Logarithmic Sobolev inequalities; Ferguson-Dirichlet process; Fleming-Viot process
 
3. Subject Subject classification Primary: 60J68; Secondary: 60J35; 28A33; 58J65; 47D07.
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Supported partially by FANEDD
 
7. Date (YYYY-MM-DD) 2011-01-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/844
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-844
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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