Spectral representations of quasi-infinitely divisible processes

Riccardo Passeggeri

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1735-1791

Abstract: This work is divided in three parts. First, we introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Second, we introduce QID stochastic integrals and present integrability conditions, continuity properties and spectral representations. Finally, we introduce QID processes, i.e. stochastic processes with QID finite dimensional distributions. For example, a process X is QID if there exist two ID processes Y and Z such that X+Y=dZ with Y independent of X. The class of QID processes is strictly larger than the class of ID processes. We provide spectral representations and Lévy–Khintchine formulations for potentially all QID processes. Many examples are presented.

Keywords: Quasi-infinitely divisible distributions; Random measure; Stochastic integral; Lévy–Khintchineformula; Signed measure (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S030441491830629X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1735-1791

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2019.05.014

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
Bibliographic data for series maintained by Catherine Liu ().