On the convex hull of symmetric stable processes

Let \alpha \in (1,2] be an \mathbb{R}^d-stable Lévy process starting at 0. We consider the closure S_t on the interval [0,t]. The first result of this paper provides a formula for certain mean mixed volumes of Z_t. The second result deals with the asymptotics of the expected volume of the stable sau...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2012-07, Vol.140 (7), p.2527-2535
Main Authors: KAMPF, JÜRGEN, LAST, GÜNTER, MOLCHANOV, ILYA
Format: Article
Language:English
Subjects:
Brownian motion
Ellipsoids
Interior points
Mathematical functions
Mathematical theorems
Random variables
Sausages
Surface areas
Symmetry
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Summary:Let \alpha \in (1,2] be an \mathbb{R}^d-stable Lévy process starting at 0. We consider the closure S_t on the interval [0,t]. The first result of this paper provides a formula for certain mean mixed volumes of Z_t. The second result deals with the asymptotics of the expected volume of the stable sausage Z_t+B is an arbitrary convex body with interior points) as t\to 0 has independent components.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2012-11128-1