Convex hulls of Levy processes

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

[img]
Preview
Text
1475266872.pdf - Published Version
Available under License Publisher holds Copyright.

Download (400kB) | Preview

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 and 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:

23 Jan 2017 11:31

Publisher DOI:

10.1214/16-ECP19

BORIS DOI:

10.7892/boris.91129

URI:

https://boris.unibe.ch/id/eprint/91129

Actions (login required)

Edit item Edit item
Provide Feedback