Exponential moments of first passage times and related quantities for Lévy processes. Issue 17 (23rd June 2015)

• Record Type: Journal Article
• Authors: Aurzada, Frank; Iksanov, Alexander; Meiners, Matthias
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 17/18(2015)
• Page Start: 1921
• Page End: 1938
• Publication Date: 2015-06-23
• Subjects: First passage time -- Inverse local time -- Last exit time -- Lévy process -- Renewal theory -- Sojourn time -- 60G51 -- 60K05; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201400289
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : For a Lévy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval ( r, ∞ ), the sojourn time in the interval ( − ∞, r ], and the last exit time from ( − ∞, r ] . Moreover, whenever these quantities are finite, we derive their respective asymptotic behavior as r → ∞ .