 Path decomposition of a reflected Lévy process on first passage over high levelsPhilip S. Griffin Stochastic Processes and their Applications, 2022, vol. 145, issue C, 29-47 Abstract: Let X be a real valued Lévy process and set Rt=Xt−infs≤tXs. This paper addresses the asymptotic behavior of the sample paths of the reflected process R on first passage over an arbitrarily high level u. We show that under the convolution equivalent condition of Klüppelberg et al. (2004), the sample paths of R on the first excursion which crosses over a high level u can be decomposed into two processes. The first describes the paths in a neighborhood of the origin. The process then takes a large jump into a neighborhood of u. The second process describes the subsequent paths. This sample path behavior is similar to that of X conditioned to cross level u. Using this connection many results concerning, for example, undershoots and overshoots can be easily obtained. Keywords: Lévy process; Reflected process; Convolution equivalence; First passage time; Overshoot (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:145:y:2022:i:c:p:29-47 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2021.11.013 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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