Molchanov, Ilya; Wespi, Florian (2016). Convex hulls of Levy processes. Electronic communications in probability, 21(69), pp. 111. Institute of Mathematical Statistics 10.1214/16ECP19

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Let X(t), t ≥ 0, be a Lévy process in Rd starting at the origin. We study the closed
convex hull Zs of {X(t) : 0 ≤ t ≤ s}. In particular, we provide conditions for the
integrability of the intrinsic volumes of the random set Zs and find explicit expressions for their means in the case of symmetric αstable Lévy processes. If the process is symmetric and each its onedimensional projection is nonatomic, we establish that the origin a.s. belongs to the interior of Zs for all s > 0. Limit theorems for the convex hull of Lévy processes with normal and stable limits are also obtained.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science 
UniBE Contributor: 
Molchanov, Ilya and Wespi, Florian 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
1083589X 
Publisher: 
Institute of Mathematical Statistics 
Language: 
English 
Submitter: 
Ilya Molchanov 
Date Deposited: 
23 Jan 2017 11:31 
Last Modified: 
05 Dec 2022 15:00 
Publisher DOI: 
10.1214/16ECP19 
BORIS DOI: 
10.7892/boris.91129 
URI: 
https://boris.unibe.ch/id/eprint/91129 