Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1)
In 1990, Bertoin constructed a measure-valued Markov process in the framework of a Bessel process of dimension between 0 and 1. In the present paper, we represent this process in a space of interval partitions. We show that this is a member of a class of interval partition diffusions introduced rece...
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| Format: | Journal article |
| Language: | English |
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Institute of Mathematical Statistics
2020
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| _version_ | 1797061178652884992 |
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| author | Winkel, M |
| author_facet | Winkel, M |
| author_sort | Winkel, M |
| collection | OXFORD |
| description | In 1990, Bertoin constructed a measure-valued Markov process in the framework
of a Bessel process of dimension between 0 and 1. In the present paper, we
represent this process in a space of interval partitions. We show that this is
a member of a class of interval partition diffusions introduced recently and
independently by Forman, Pal, Rizzolo and Winkel using a completely different
construction from spectrally positive stable L\'evy processes with index
between 1 and 2 and with jumps marked by squared Bessel excursions of a
corresponding dimension between $-2$ and 0. |
| first_indexed | 2024-03-06T20:27:21Z |
| format | Journal article |
| id | oxford-uuid:2fd5b4cc-c6a9-4494-a136-04b9db1b50e0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:27:21Z |
| publishDate | 2020 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:2fd5b4cc-c6a9-4494-a136-04b9db1b50e02022-03-26T12:57:53ZDiffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1)Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2fd5b4cc-c6a9-4494-a136-04b9db1b50e0EnglishSymplectic ElementsInstitute of Mathematical Statistics2020Winkel, MIn 1990, Bertoin constructed a measure-valued Markov process in the framework of a Bessel process of dimension between 0 and 1. In the present paper, we represent this process in a space of interval partitions. We show that this is a member of a class of interval partition diffusions introduced recently and independently by Forman, Pal, Rizzolo and Winkel using a completely different construction from spectrally positive stable L\'evy processes with index between 1 and 2 and with jumps marked by squared Bessel excursions of a corresponding dimension between $-2$ and 0. |
| spellingShingle | Winkel, M Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title | Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title_full | Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title_fullStr | Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title_full_unstemmed | Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title_short | Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1) |
| title_sort | diffusions on a space of interval partitions construction from bertoin s bes0 d d ∈ 0 1 |
| work_keys_str_mv | AT winkelm diffusionsonaspaceofintervalpartitionsconstructionfrombertoinsbes0dd01 |