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The convex minorant of the Cauchy process


Bertoin, Jean (2000). The convex minorant of the Cauchy process. Electronic Communications in Probability, 5(5):51-55.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:20 January 2000
Deposited On:25 Jul 2013 06:36
Last Modified:05 Apr 2016 16:52
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
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

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