Molchanov, Ilya; Wespi, Florian (2016). Convex hulls of Levy processes. Electronic communications in probability, 21(69), pp. 1-11. Institute of Mathematical Statistics 10.1214/16-ECP19
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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 α-stable Lévy processes. If the process is symmetric and each its one-dimensional projection is non-atomic, 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, Wespi, Florian |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1083-589X |
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: |
10.1214/16-ECP19 |
BORIS DOI: |
10.7892/boris.91129 |
URI: |
https://boris.unibe.ch/id/eprint/91129 |
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