 Change-level detection for Lévy subordinatorsZeina Al Masry, Landy Rabehasaina and Ghislain Verdier Stochastic Processes and their Applications, 2022, vol. 147, issue C, 423-455 Abstract: Let X=(Xt)t≥0 be a process behaving as a general increasing Lévy process (subordinator) prior to hitting a given unknown level m0, then behaving as another different subordinator once this threshold is crossed. This paper addresses the detection of this unknown threshold m0∈[0,+∞] from an observed trajectory of the process. These kind of model and issue are encountered in many areas such as reliability and quality control in degradation problems. More precisely, we construct, from a sample path and for each ε>0, a so-called detection level Lε by considering a CUSUM inspired procedure. Under mild assumptions, this level is such that, while m0 is infinite (i.e. when no changes occur), its expectation E∞(Lε) tends to +∞ as ε tends to 0, and the expected overshoot Em0([Lε−m0]+), while the threshold m0 is finite, is negligible compared to E∞(Lε) as ε tends to 0. Numerical illustrations are provided when the Lévy processes are gamma processes with different shape parameters. Keywords: Change detection; Lévy process; Subordinator; CUSUM; Sequential testing (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:147:y:2022:i:c:p:423-455 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.01.022 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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