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Bertoin, Jean (2000). The convex minorant of the Cauchy process. Electronic Communications in Probability, 5(5):51-55.
We determine the law of the convex minorant (Ms,s∈[0,1]) of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that the paths of M have a continuous derivative, and that the support of the Stieltjes measure dM′ has logarithmic dimension one.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty |
| Language: | English |
| Date: | 20 January 2000 |
| Deposited On: | 25 Jul 2013 06:36 |
| Last Modified: | 09 Jan 2025 02:42 |
| Publisher: | Institute of Mathematical Statistics |
| ISSN: | 1083-589X |
| OA Status: | Gold |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1214/ECP.v5-1017 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1747095 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0954.60042 |
Bertoin, Jean