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Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
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Lie, Han Cheng and Sullivan, T. J. (2018) Quasi-invariance of countable products of Cauchy measures under non-unitary dilations. Electronic Communications in Probability, 23 . 8. doi:10.1214/18-ECP113
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Official URL: http://dx.doi.org/10.1214/18-ECP113
Abstract
Consider an infinite sequence (Un)n∈N of independent Cauchy random variables, defined by a sequence (δn)n∈N of location parameters and a sequence (γn)n∈N of scale parameters. Let (Wn)n∈N be another infinite sequence of independent Cauchy random variables defined by the same sequence of location parameters and the sequence (σnγn)n∈N of scale parameters, with σn≠0 for all n∈N. Using a result of Kakutani on equivalence of countably infinite product measures, we show that the laws of (Un)n∈N and (Wn)n∈N are equivalent if and only if the sequence (|σn|−1)n∈N is square-summable.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science > Engineering Faculty of Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Cauchy problem, Differential equations, Partial, Quasi-metric spaces, Infinite | ||||||
| Journal or Publication Title: | Electronic Communications in Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1083-589X | ||||||
| Official Date: | 21 February 2018 | ||||||
| Dates: |
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| Date of first compliant deposit: | 15 April 2020 | ||||||
| Volume: | 23 | ||||||
| Article Number: | 8 | ||||||
| DOI: | 10.1214/18-ECP113 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Publisher Statement: | "The right to place the final version of this article Lie, Han Cheng and Sullivan, T. J. (2018) Quasi-invariance of countable products of Cauchy measures under non-unitary dilations. Electronic Communications in Probability, 23. 8. on their own homepage or in a public digital repository, provided there is a link to the official journal site." | ||||||
| Access rights to Published version: | Open Access | ||||||
| RIOXX Funder/Project Grant: |
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