On exact Hausdorff measure functions of operator semistable Lévy processes. Issue 6 (2nd November 2017)

• Record Type: Journal Article
• Authors: Kern, Peter; Wedrich, Lina
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 6(2017)
• Page Start: 980
• Page End: 1006
• Publication Date: 2017-11-02
• Subjects: Operator semistable Lévy process -- sample path -- range -- semi-selfsimilarity -- exact Hausdorff measure -- gauge function -- expected sojourn time -- semistable subordinator -- Tauberian theorem; 60G51 -- 28AG78 -- 28A80 -- 60G17 -- 60G18 -- 60G52; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1344556
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: Let X = { X ( t )} t ⩾ 0 be an operator semistable Lévy process on with exponent E, where E is an invertible linear operator on . In this article, we determine exact Hausdorff measure functions for the range of X over the time interval [0, 1] under certain assumptions on the principal spectral component of E . As a byproduct, we also present Tauberian results for semistable subordinators and sharp bounds for the asymptotic behavior of the expected sojourn times of X .