A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions
We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson–Dirichlet(α,θ) distributions, for α∈(0,1) and θ≥0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields...
| Prif Awduron: | , , , |
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| Fformat: | Journal article |
| Iaith: | English |
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Institute of Mathematical Statistics
2022
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| _version_ | 1826307887775875072 |
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| author | Forman, N Rizzolo, D Shi, Q Winkel, M |
| author_facet | Forman, N Rizzolo, D Shi, Q Winkel, M |
| author_sort | Forman, N |
| collection | OXFORD |
| description | We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson–Dirichlet(α,θ) distributions, for α∈(0,1) and θ≥0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields 148 (2010) 501–525). We build on our previous work on (α,0)- and (α,α)-interval partition evolutions. The extension to general θ≥0 is achieved by the construction of a σ-finite excursion measure of a new measure-valued branching diffusion. Our measure-valued processes are Hunt processes on an incomplete subspace of the space of all probability measures and do not possess an extension to a Feller process. In a companion paper, we use generators to show that ranked masses evolve according to a two-parameter family of diffusions introduced by Petrov (Funktsional. Anal. i Prilozhen. 43 (2009) 45–66), extending work of Ethier and Kurtz (Adv. in Appl. Probab. 13 (1981) 429–452). |
| first_indexed | 2024-03-07T07:11:21Z |
| format | Journal article |
| id | oxford-uuid:c91176f8-cc7c-40e0-9fa6-9788084767bc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:11:21Z |
| publishDate | 2022 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:c91176f8-cc7c-40e0-9fa6-9788084767bc2022-06-16T10:05:30ZA two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c91176f8-cc7c-40e0-9fa6-9788084767bcEnglishSymplectic ElementsInstitute of Mathematical Statistics 2022Forman, NRizzolo, DShi, QWinkel, MWe give a pathwise construction of a two-parameter family of purely-atomic-measure-valued diffusions in which ranked masses of atoms are stationary with the Poisson–Dirichlet(α,θ) distributions, for α∈(0,1) and θ≥0. These processes resolve a conjecture of Feng and Sun (Probab. Theory Related Fields 148 (2010) 501–525). We build on our previous work on (α,0)- and (α,α)-interval partition evolutions. The extension to general θ≥0 is achieved by the construction of a σ-finite excursion measure of a new measure-valued branching diffusion. Our measure-valued processes are Hunt processes on an incomplete subspace of the space of all probability measures and do not possess an extension to a Feller process. In a companion paper, we use generators to show that ranked masses evolve according to a two-parameter family of diffusions introduced by Petrov (Funktsional. Anal. i Prilozhen. 43 (2009) 45–66), extending work of Ethier and Kurtz (Adv. in Appl. Probab. 13 (1981) 429–452). |
| spellingShingle | Forman, N Rizzolo, D Shi, Q Winkel, M A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title | A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title_full | A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title_fullStr | A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title_full_unstemmed | A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title_short | A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions |
| title_sort | two parameter family of measure valued diffusions with poisson dirichlet stationary distributions |
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